a person walking along a straight road observes that at two consecutive kilometer stones, the angles of elevation of a hill in front of him are 30degree and 45 degree find the height of the hill

Answers

Answer 1

First, you need to draw the situation: you have three points on a straight line, A is the first kilometer stone, B is the second one and C is the foot of the hill. Let's call H the top of the hill. Connecting H with both A and B you get two triangles rectangle (BCH and ACH).

The triangle rectangle BCH has one other angle that is 45°, which means that it is an isosceles triangle, therefore BC = HC = height of the hill (h).

Now, consider the triangle ACH: it has an angle of 30° (which means that the other angle is 60°) and AC = BC + AB = h + 1 (where we considered h measured in km).
In such a particular triangle (30°- 60°- 90°), the ratio between the long and the short leg is √3, which means that:
√3·HC = AC

We can then write:
√3·h = (h + 1)

which can be solve for h:
√3·h - h = 1
h(√3 - 1) = 1
h =1/ (√3 - 1)

We can rationalize:
h =  [tex] \frac{1}{ \sqrt{3} - 1} \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1 } [/tex]
   = (√3 + 1) / 2
   = 1.366 km

Therefore the correct answer is: the hill is 1.366km high

Related Questions

WXYZ is an isosceles trapezoid with legs WX and YZ and a base XY. If the length of WX is 6x+5, the length of XY is 10x+4 and the length of YZ is 8x-3, find the VALUE OF Y.

Answers

Be more specific. Like what is it asking you to do ? I'm trying to help. :)

Given is an isosceles trapezoid WXYZ such that WX and YZ are legs of trapezoid with base XY. Also given are the measurements of trapezoid as follows :-

Legs WX = 6x + 5 and YZ = 8x - 3

Base XY = 10x + 4

we know the fact :- "For an isosceles trapezoid, its legs are congruent".

If it is asking for value of the variable 'x', then we can set the expressions of its legs equal and solve for x.

Leg WX = Leg YZ

6x + 5 = 8x - 3

8x - 6x = 5 + 3

2x = 8

x = 4

so, x = 4 would be the answer.

If it is asking for value of base XY, then we could plug the value of x in the expression of XY and compute.

Base XY = 10x + 4

XY = 10(4) + 4

XY = 40 + 4

XY = 44

so, base XY = 44 would be the answer.

A road map has a scale of 1:20000 on the map a road has a length of 4cm work out the actual distance five your answer in metre

Answers

Final answer:

To determine the actual distance of a 4 cm road on a map with a 1:20000 scale, multiply the map measurement by the scale factor to get 80000 cm, then convert it to meters to obtain an actual distance of 800 meters.

Explanation:

To work out the actual distance of a road on a map that has a scale of 1:20000, you need to convert the map length to the actual length. If the road measures 4 cm on the map, you would use the following steps:

Determine the scale ratio, which is 1 cm on the map represents 20000 cm in reality.Multiply the map distance by the scale factor. In this case:
4 cm (map distance) imes 20000 (scale factor) = 80000 cm. Convert the result from centimeters to meters since 1 meter is equal to 100 centimeters.
80000 cm \/ 100 = 800 meters.

Therefore, the actual distance of the road is 800 meters.

a bottle of hand lotion is on sale for $2.25 . If this price represents a 50% discount from the original price , what is the original price to the nearest cent ?

Answers

so 2.25 is 50% of the original price
let's write original price as x
50% of x = 2.25
0.5 * x = 2.25
divide both sides by 0.5
x = 4.5

The original price is 4.5

To check:
50% * (4.5) =?= 2.25
0.5 * 4.5 =?= 2.25
2.25 = 2.25

Hope this helps.

Answer:

$4.50

Step-by-step explanation:

Since there is a 50 % discount on the price, the new price is 100 % − 50 % = 50 % of the original price.

Let the original price be x . Then we have:

x ⋅ 50 % = $ 2.25

x ⋅ 1 2 = $ 2.25

x = $ 2.25 ⋅ 2 =

$ 4.50

So, the bottle of hand lotion's original price was $ 4.50 .

Mr. Jacobs is going to make a histogram of the test scores from the last math test he gave. He plans to first organize the data into a stem-and-leaf plot and then make the histogram from the stem-and-leaf plot. The test scores are listed below. 79, 82, 65, 61, 94, 97, 84, 77, 89, 91, 90, 83, 99, 71, 68, 77, 87, 85 Which of the following expressions could be used to find how many students scored less than a 90 on the test?
3 + 44 + 63 + 4 + 63 + 4 + 6 + 1

Answers

The stem and leaf plot will look like:
6 | 1 5 8 - 3 scores
7 | 1 7 7 9 - 4 scores
8 | 2 3 4 5 7 9 - 6 scores
9 | 0 1 4 7 9 - 1 score
To total up the number of students who scored less than 90, we have 3 under 60-69, 4 under 70-79, and 6 under 80-89, so this is 3 + 4 + 6. This is the third choice.

Answer:

The answer is 3 + 4 + 6

There are 13 numbers that are lower than 90, and 3 + 4 + 6 is the correct expression because 3 + 4 + 6 = 13.

I did this on my lesson and I got it right.

The Georgia sales tax is 4%. However, some places in Georgia charge a higher rate of sales tax. This is MOST LIKELY because Question 3 options: shipping goods to some localities in Georgia can be extremely expensive. the sales tax in Georgia is determined by how much money the buyer makes per year. localities in Georgia can add a certain percentage to sales tax for their own needs. sellers can charge whatever they want as long as the minimum state rate is collected.

Answers

The answer is, localities in Georgia can add a certain percentage to sales tax for their own needs.

Final answer:

The most likely reason some localities in Georgia charge higher sales taxes is that they can add to the state's 4% tax to cater to their own financial needs, funding local services and needs.

Explanation:

The question relates to why some places in Georgia might charge a higher rate of sales tax than the state's baseline of 4%. The most likely reason is that localities in Georgia have the authority to add additional percentages to the state sales tax to address their individual financial requirements. This is commonly seen in states where local governments utilize the sales tax mechanism to fund specific local public services and projects. For instance, a city may add a percentage to fund improvements in education, transportation, or healthcare facilities.

The amount of sales tax is determined by multiplying the price of the goods or services by the sales tax rate. When a locality opts to add to the state sales tax, the total sales tax a consumer pays is the sum of the state rate plus any local rates. This system allows for local governments to cater to their unique budgetary needs while still adhering to the broader state tax structure. This is different from other variables, like shipping costs, buyer's income, or seller preferences, which do not generally affect the sales tax rate.

Over several months, a meteorologist recorded a total snowfall of 8.6 centimeters. During this period, the average monthly snowfall was 4.3 centimeters. For how many months did the meteorologist collect measurements of the snowfalls?

Answers

He recorded the snowfall for 2 months

{(6,-6), (7, -6), (8, -6), (9,-6)}

EXPLAIN whether or not the following relations is a function.

Answers

this is a function because every input has one output, the x values don't repeat itself meaning its a function.

An economy package of cups has 200 green cups. If the green cups are 10% of the total package, how many cups are in the package?

Answers

Final answer:

Set up a proportion where 10% of the total number of cups equals 200 green cups, then calculate to find that there are 2000 cups in the entire package.

Explanation:

To find the total number of cups in the package when 200 green cups represent 10% of the total, we can set up a simple proportion. Here, 10% corresponds to the number of green cups we know about. We need to find 100% to discover the total number of cups in the package.

The proportion we'll set up is:

10% / 200 cups = 100% / x cups

To solve for x (the total number of cups), we will divide 200 cups by 10% to find the value of 1% and then multiply by 100%:

1% of total = 200 cups / 10

x (total cups) = (200 cups / 10) × 100

Perform the calculation:

x = 20 cups × 100

x = 2000 cups

So, there are 2000 cups in the total package.

A triangular prism and two nets are shown:

Which is the correct net of the prism and what is the surface area of the prism?

Answers

the correct net of the prism is Net A
surface area of the prism is
Surface area = Area of two triangular faces + Area of bottom rectangle + Area of two side rectangles

View attachment

Hope this helps

The correct net of the prism is net A and the surface area of the prism is 510 square inches

How to determine the surface area

To calculate the area of the triangular prism, we make use of the net A

Start by calculating the area of the rectangle.

The dimension of the rectangle is (5 + 12 + 13) by 15

So, the area of the rectangle is:

[tex]Area = (5 + 12 + 13) * 15[/tex]

[tex]Area = 450[/tex]

Next, calculate the area of the two congruent triangles of base 5 and height 12

[tex]Area = 2 * 0.5 * (5 * 12)[/tex]

[tex]Area = 60[/tex]

Sum both areas

[tex]Total = 450 + 60[/tex]

[tex]Total = 510[/tex]

Hence, the surface area of the prism is 510 square inches

Answers

what grade level are u in because i can try to help but it will take me a few minutes

1. Answer:x=12
2. Answer:
[tex] \frac{18}{7} [/tex]
3. Answer:
x= -3

Hope this Helps! ♥

Semi annually means how many times a year?

Answers

Biannual and semiannual can be used interchangeably; they both mean “twice a year.” But biennial describes something that occurs every two years.

Felicia bought 4 buckets of popcorn at the movies if she paid a total of $15 how much is one bucket of popcorn?

Answers

15/4 = $3.75 per bucket

Divide 15 and 4 together

15/4 = 3.75

Each book cost ~$3.75

hope this helps

A shopping company charges $3.50 plus $0.85 per pound to ship a package. Janet shipped a package and the total charge was $8.60. Write and solve an equation to find the weight of the package.

Answers

3.50 +.85p=8.60
Basically replaced p with any number than times that your outcome of that number add it to 3.50 and see if you get 8.60

Based on the information, the weight of the package is approximately 6 pounds.

How to calculate the weight

According to the given information, the shopping company charges $3.50 as a base fee and an additional $0.85 per pound to ship the package.

The total charge for shipping the package, which is $8.60, can be expressed as:

$3.50 + ($0.85 * w) = $8.60

To find the weight of the package, we need to solve this equation for "w". Let's solve it step by step:

$0.85 * w = $8.60 - $3.50

$0.85 * w = $5.10

Now, we can isolate "w" by dividing both sides of the equation by $0.85:

w = ($5.10) / ($0.85)

w ≈ 6

Therefore, the weight of the package is approximately 6 pounds.

Learn more about equations

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The image on a movie poster was shrunk to make the DVD cover art for the movie, so that the cover art is a scale image of the poster. The poster is 36 inches wide, and the DVD cover art is 6 inches wide. If the diagonal of the poster is 4 feet, what is the diagonal of the DVD cover art?

Answers

Please see the attached image for a visual representation of our scale factor. We can set up this proportion by taking the DVD cover and poster values and placing them in fractions. Cross multiply and divide to solve for x.

The first thing we need to do is find the proportionality constant [tex]k[/tex]. Since we now that the width of a movie poster was shrunk from 36 inches to 6 inches to make the DVD cover, [tex]k= \frac{36}{6} =6[/tex]; therefore, the width of poster was shrunk, in other words divided, by a factor of 6.
Now that we have our proportionality constant lest apply it to the diagonal of the poster to find the diagonal of the DVD cover. But notice that the diagonal of the poster is in feet not inches, so we need to convert 4 feet to inches first. Remember that 1 foot = 12 inches, so lets use that proportion to set up our conversion fraction:
[tex](4feet)( \frac{12inches}{1 foot} )= 48inches[/tex]
The only thing left now is shrunk, divide, the diagonal by our proportionality constant [tex]k[/tex]
[tex] \frac{48}{k} = \frac{48}{6} =8[/tex]

We can conclude that If the diagonal of the poster is 4 feet, the diagonal of the DVD cover will be 8 inches.

-1/5 of a number is n is at least 17

Answers

-1/5 * n ≤ 17

n ≥ -17/5 is the answer

Elmo buckets made 54 out of 80 free throw .What percent did he miss

Answers

Answer:

67.50%

Step-by-step explanation:

We can prove that the answer is correct by taking 67.50 percent of 80 to get 54:

(80 x 67.50)/100 = 54

Note that our calculator rounds the answers up to two decimals if necessary. Once again, the answer is as follows:

67.50%

1.2 decreased by 40%

Answers

1.2 x 0.4 = 0.48
1.2 - 0.48 = 0.72
Solution = 0.72

I hope this helps

0.72 is the answer.

Rectangle???ABCD has vertices A(8, 5) , B(8, 10) , C(14, 10) , and D(14, 5) . A dilation with a scale factor of 1.2 and centered at the origin is applied to the rectangle. Which vertex in the dilated image has coordinates of (9.6, 6) ?

A???

B???

C???

D???

Answers

A (8, 5)

hope this helps!

Explain the advantage of creating a linear function from a set of data; why bother to do this?

Answers

If the data you list has a linear relationship, then creating a linear function from the data might be helpful because it would define the relationship and help you to answer questions related to it that the data you have at present might not.

Here is an example. Height and shoe size have a linear relationship. Let's say you plot the point (height in inches, shoe size in US women's sizes) for 50 people or so. You would see a strong linear relationship. The points wouldn't make a perfect line but very close to it. As height increases so does shoe size and it does so in a linear way. Now if we call the height h and the shoe size s then we would have an equation that relates h and s. So that if we wanted to know the shoe size of someone 96 inches (8 feet high) tall we could get that (or very close to it) from the equation even if there was no one in our sample that was that tall. Similarly we could solve for height if we knew shoe size.

Show 39c in two ways

Answers

1) 39 pennies

2) 1 quarter, 1 dime, 4 pennies.

3) 2 dimes, 3 nickels, 4 pennies.

Hey there!

First way: 1 quarter and 14 pennies. (25 + 14 = 39)

Second way: 3 dimes and 9 pennies ( 3 x 10 = 30 and 30 + 9 = 39)

These are both ways that equal 39 cents.

Hope this helps you.
Have a great day!

Explain how the scale factor is calculated and how the numerical value of the scale factor differs for enlargements and reductions.

Answers

Answer: The scale factor is the ratio of the scale figure dimensions to the original dimensions. The scale factor for an enlargement is a number greater than 1. The scale factor for a reduction is a decimal or fraction between 0 and 1.

HOPE THIS HELPS!!!!

Answer:

According to the scale factor, the original dimensions are smaller than the scaled figures. An enlargement's scale factor is a number greater than one. A reduction's scale factor is a decimal or fraction between 0 and 1.

Step-by-step explanation: changed up the sample answer ^^

complete the following math problem
3+6×3=

Answers

21
3+(6*3)
Hope that helps!

Remember PEMDAS
Do multiplication first: 6*3=18
Then do addition: 3+18=21
So your answer is 21.

Approximate the length of the diagonal of the square to the nearest tenth. the square sides are 6

Answers

6*sqrt2 which is the same as 8.5

NEED HELP FAST PLEASE!! Draw the base plan for the set of stacked cubes, assume the no cubes are hidden from view.

Answers

Assuming no cubes are hidden from view, the base view (as if you're looking from underneath the figure) would have a 2 x 2 square of cubes, plus one at the top. This means that your correct choice would be the one I've attached.

Use algebra tiles to model and solve x+5=3x-1

Answers

x + 5 = 3x - 1
x - 3x = -1 -5
-2x = -6
2x = 6
x= 6÷ 2
x = 3

The question asks that you use algebra tiles to model and solve the equation [tex]x+5=3x-1[/tex]. I set up the scenario digitally (see attached image).

Whatever blocks you have on both sides you can cancel. So we cancel one [tex]x[/tex]-block, and to take away the [tex]-1[/tex]-block, we balance the equation by putting a [tex]+1[/tex]-block on the other side. We are left with 2 [tex]x[/tex]-blocks equal to 6 [tex]+1[/tex]-blocks. This is equivalent to 1 [tex]x[/tex]-bock equal to 3 [tex]+1[/tex] blocks, so [tex]x=3[/tex].

Algebraically, you can write
[tex]x+5=3x-1 \\ 5=2x-1 \\ 6=2x \\ x=3[/tex].
I personally find the latter approach much easier, but I think the tiles are a nice way to conceptualize what you're doing.

Ravi is driving 440 miles to visit his grandma. He drives at a rate of 55 miles per hour. How many hours will it take him to get 34 of the way there?

Answers

you answer is about one hour i guess

Answer:

The answer is 6 hours

Step-by-step explanation:

;)

rename each mixed number as an equivalent mixed number with the same denominator. 4 6/9= 7 5/3= 3 7/8= 5 19/14=

Answers

4 6/9= 38/9
7 5/3= 26/3
3 7/8= 31/8
5 19/14 =89/14

Final answer:

To rename mixed numbers with the same denominator, we simplify the fractions where the numerator is larger than the denominator by dividing the numerator by the denominator and expressing the remainder as a fraction. The simplified mixed numbers for the examples are 4 6/9, 8 2/3, 3 7/8, 6 5/14.

Explanation:Renaming Mixed Numbers To Have The Same Denominator

To rename each mixed number as an equivalent mixed number with the same denominator, you first must understand that the denominator is the bottom number in a fraction. To make two fractions have the same denominator, you need to find the least common denominator (LCD). The LCD is the least common multiple of the two denominators.

Let's walk through on how this works for the provided numbers:

4 6/9: The fraction here is already simplified. So, it remains the same, i.e., 4 6/97 5/3: Here, the numerator is larger than the denominator. So, we simplify the fraction 5/3 by dividing 5 by 3 which gives 1 remainder 2. So, it becomes 7 1/3 + 2/3 and further simplifies to 8 2/3.3 7/8: The fraction here is already simplified. So, it remains the same, i.e., 3 7/85 19/14: Here, the numerator is larger than the denominator. So, we simplify the fraction 19/14 by dividing 19 by 14 which gives 1 remainder 5. So, it becomes 5 1/14 + 5/14 and further simplifies to 6 5/14.

So, the mixed numbers with the same denominator are 4 6/9, 8 2/3, 3 7/8, 6 5/14.

Learn more about Renaming Mixed Numbers

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The distance around a circle is 56.55 meters long. What is the diameter of the circle?

Answers

the answer is 113.1 I hope it helps you and I hope this is correct.

Answer: Diameter of circle = 18m

Explanation:

Given that distance around a circle is = 56.55 meter

The distance around a circle on the other hand is called the circumference .

That means Circumference = 56.55 m

We know the formula of circle's circumference= 2πr

where r is the radius and 2r is diameter of the circle

So,

2πr = 56.55

divide by π both the side

2r = [tex] \frac{56.55*7}{22} [/tex]

Value of π = [tex] \frac{22}{7} [/tex]

2r = 17.993 ≈ 18 m

Diameter of circle = 18m

What’s the answer? Thank You

Answers

33 square inches --> straight line across
25 square inches --> straight line across

I DONT KNOW ASK SOMEONE ELSE BROOOOOOOOOO

which names the opposite and absolute value of 12

Answers

Opposite: -12
Absolute value: |12| = 12

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