The sun is 25 degrees above the horizon. find the length of a shadow cast by a building that is 100 feet tall. round your answer to two decimal places. the length of the shadow is ____ feet.
Answers
214.45 feet
Explanation
The sun is 250 above the horizon. This means that the angle of elevation is 25o.
Since you have been given the height of the building, you can use the trigonometric ratio (tangent) to find the length of the shadow (l).
tan〖= 〗 oposite/adjacent
tan25=100/l
l=100/tan25 =214.4506921
Length of the shadow = 214.4506921 feet
Answer:
214.45 feet.
Step-by-step explanation:
Please find the attachment.
Let x be the length of building's shadow.
We have been given that the sun is 25 degrees above the horizon. The length of the building is 100 feet tall.
We can see from our attachment that the length of the building is opposite side and the length of the shadow is adjacent side for the angle of 25 degrees.
Since tangent relates the opposite side of right triangle with adjacent side, so we can set an equation to find the length of building's shadow as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(25^{\circ})=\frac{100}{x}[/tex]
[tex]x=\frac{100}{\text{tan}(25^{\circ})}[/tex]
[tex]x=\frac{100}{0.466307658155}[/tex]
[tex]x=214.45069\approx 214.45[/tex]
Therefore, the length of shadow cast by the building is 214.45 feet.
Related Questions
A shoe box measures 15in. by 7 in. by 4 1/2 in. What is the surface area of the box?
Answers
4 1/2----> (4*2+1)/2-----> 9/2
[surface area of the box]=2*[area of the base]+[perimeter of the base*height]
[area of the base]=15*7------> 105 in²
perimeter of the base=2*(15+7)-----> 44 in
[surface area of the box]=2*[105]+[44*9/2]----> 210+198---> 408 in²
the answer is
408 in²
A parallelogram has an area of
144
144
square centimeters. If the base measures
24
24
centimeters, what is the height?
Answers
A rectangular prism has a length of 5 cm, a width of 212 cm, and a height of 112 cm. Which expressions can be used to find the volume of the prism? Select each correct answer. A. 5∙212∙112 B. 1212∙112 C, 112(5+212) D. 12(1212∙112)
Answers
Volume is the amount of 3-dimensional space an object occupies
Volume is measured in cubic units.To find Volume Multiply the length, the width, and the height.
The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W.
The rectangular prism has a length of 5 cm, a width of 212 cm, and a height of 112 cm.
Substituting these values in the formula.
Volume = 5∙212∙112
Option A. 5∙212∙112 is the right answer.
What is the measure of ∠D ?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠D=
°
Answers
NEED HELP AS FAST AS POSSIBLE
Dan drew the line of best fit on the scatter plot shown below:
A graph is shown with scale along x axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 15 at increments of 1 and scale along y axis from 0 to 15 at increments of 1. The ordered pairs 0, 4 and 1, 4 and 2, 5 and 3, 6 and 4, 7 and 5, 9 and 6, 10 and 7, 11 and 8, 13 and 9, 14 and 10, 15 are shown on the graph. A straight line joins the ordered pairs 0, 3 and 10, 15.
What is the equation of this line of best fit in slope-intercept form?
y = 3x + 6 over 5
y = 5 over 6x + 3
y = 3x + 5 over 6
y = 6 over 5x + 3
Answers
Answer:
d
Step-by-step explanation:
y=6/5x+3
a circle has a diameter of 10cm what is the best proximation of this area use 3.14 to approximate for pi
Answers
The answer would be [tex] 75.8^{cm2} [/tex]
Hope this helped!
On this exercise is given that a circle has a diameter of 10cm and it is asked to find its area, as previous said the only way to find the area of a circle is to use the formula A=πr^2, but on this case the radius is not given. As result you have to divide the measurement of the diameter by two, and the number found represents the radius.
10cm/2= 5cm The radius of the circle is 5cm.
Now that the radius is known you can substitute the values in the formula to find the area of the circle.
A=πr^2
A=(3.14)(5)^2
A=(3.14)(25)
A=78.5 cm^2
The area of the circle is 78.5 square centimeters.
3 consecutive odd numbers whose sum is -63
Answers
Answer:
-23, -21, -19
Step-by-step explanation:
The middle one is the average of the three: -63/3 = -21. The others are 2 units either side of this one.
Point P' is the image of P(3, 5), under a reflection across the y-axis. What are the coordinates of P'?
Answers
.. P' = (-3, 5)
Answer:
P'( -3 ,5).
Step-by-step explanation:
Given : Point P' is the image of P(3, 5), under a reflection across the y-axis.
To find : What are the coordinates of P'
Solution : We have given
Pre image P( 3 ,5 ).
Rule of reflection over y axis : ( x ,y) →→→( -x , y) .
Here , x = 3 ; y = 5
Then , ( 3 ,5) →→→( -3 , 5) .
Therefore, P'( -3 ,5).
Jerry jogs the same round trip path everyday. He jogs 0.7 miles to the park and then 0.5 miles from the park to the playground. After getting a drink at the playground, he then jogs back from the playground to his house. He jogs from the playground to the bridge 0.3 miles and then 0.9 miles from the bridge to his house. When Jerry completes his jog, how many miles is he from his house?
Answers
Answer:
He will be 0 miles from his house.
Step-by-step explanation:
Since, he jogs the same round trip path.
Thus,
[tex]\text{His final distance from his house }=d_1-d_2[/tex]
Where, [tex]d_1[/tex] = The distance he covered in first trip (towards playground)
[tex]d_2[/tex] = The distance he covered in second trip (towards house),
In his first trip,
He covered 0.7 miles to the park and then 0.5 miles from the park to the playground.
[tex]d_1 = 0.7 + 0.5 = 1.2\text{ miles}[/tex],
In his second trip,
He covered 0.3 miles to the bridge and then 0.9 miles from the bridge to his house
[tex]d_2 = 0.3 + 0.9 = 1.2\text{ miles}[/tex],
[tex]\text{His final distance from his house }=1.2-1.2=0\text{ miles}[/tex]
Help with this math question pleaseee!!!
Answers
But in this case the parent function is transformed. It is shifted vertically upward by 4 units. When an exponential function is shifted vertically up or down its asymptote is also shifted by same number of units.
Hence, the asymptote of [tex]f(x)= 3^{x}+4 [/tex] will be shifted 4 units above as compared to the asymptote of [tex]f(x)= 3^{x} [/tex] .Therefore, the asymptote of [tex]f(x)= 3^{x}+4 [/tex] is y=4
In Queensland, approximately 32% of household waste is recycled. What are the factors of 32?
Answers
32 = 2^5 . . . . . the only prime factor is 2. It has multiplicity 5.
32 = 1*32 = 2*16 = 4*8
Divisors of 32 are 1, 2, 4, 8, 16, 32.
two-thirds of the children in the fourth grade class are girls. if there are 14 girls, what is the total number of children in the class
Answers
What is the value of m in the figure below?
Answers
Answer: square root of 136
Step-by-step explanation:
Which conversion requires division? Use the metric table to help answer the question.
Answers
Like Centimeter to Meter
Like Meter to Kilometer
Like Feet to Mile
Like Yard to Mile
Like Feet to Yard
12000 feet divided by 3 is 4000, so 4000 yards, that kid of thing
Answer:
Which conversion requires division? Use the metric table to help answer the question.
D) decigrams to dekagrams
Step-by-step explanation:
Please help me with this question. I will give 10 points and brainliest :) I beg you! I need this right!
Answers
I hope this helps! :)
Find the inverse function of f(x) . F(x) = 7x - 9
Answers
The inverse of this function is f(x) = [tex] \frac{x + 9}{7} [/tex].
All inverse functions can be found by switching the x and f(x) values. Then you can solve for the new f(x). The result is the inverse function. Below is the step-by-step process for finding one.
f(x) = 7x - 9 ----> Switch the x and f(x)
x = 7f(x) - 9 -----> Add 9 to both sides
x + 9 = 7f(x) ----> Divide both sides by 7
f(x) = [tex] \frac{x + 9}{7} [/tex]
Which terms accurately classify this triangle? CHOOSE EXACTLY TWO ANSWERS that are correct. A. right B. acute C. isosceles D. scalene
Answers
You can also notice the two lines entering 2 sides of the triangle, these lines mean that these two sides are equal since there are only 2 equal sides your triangle is an isosceles
Your 2 choices are; B. Acute and C. Isosceles
help me asap
Which equation has both 7 and -7 as possible values of y ?
y³=42
y²=42
y³=49
y²=49
Which equation has both 4 and ? –4 as possible values of y ?
y²=8
y³=12
y²=16
y³=64
Answers
With this in mind, you expect to be looking for squares in answer to your question. You will find them.
1) y² = 49 . . . . . . . 4th selection
2) y² = 16 . . . . . . . 3rd selection
How many triangles exist with the given angle measures? 40 25 115
Answers
Hope this helps!!:)
Have a good day!!:D
Plz mark brainliest!!XD
Multiple triangles can exist within the given angle measures.
Hope I helped!
Let me know if you need anything else!
~ Zoe
What change do you have to make to the graph of f (x) = 7x in order to graph the function g (x) = 7x+10?
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}[/tex]
[tex]\bf ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]
now, with that template in mind, let's see
[tex]\bf \stackrel{parent}{f(x)=7x}\qquad \qquad \qquad \stackrel{transformed}{g(x)=7x\stackrel{D}{+10}}[/tex]
D = 10, upwards shift of 10 units.
Final answer:
To graph g(x) = 7x+10 from f(x) = 7x, shift the entire line upwards by 10 units to adjust for the new y-intercept of 10 while maintaining the same slope of 7.
Explanation:
To graph the function g(x) = 7x+10 based on the graph of f(x) = 7x, you need to alter the y-intercept. Original function f(x) is a straight line with a slope of 7 and a y-intercept of 0. However, function g(x) has the same slope of 7 since the coefficient of x is the same, but the y-intercept is increased by 10. This means that you need to shift the entire line of f(x) upwards by 10 units on the y-axis.
Start by placing a point at (0,10) on the graph to represent the new y-intercept. Then, using the slope of 7, for every 1 unit you move to the right on the x-axis, move 7 units up to plot another point. Repeat this process for a few more points to get an accurate line, and then draw a straight line through your points to complete the graph of g(x).
Don Price bought a house for $70,000. He rents the house for $900 per month. He has $700 in monthly expenses.
What is the amount of the annual rent?
What is the amount of annual expenses?
What is his rate of income to the nearest tenth of a percent?
Answers
Annual Expenses=$8,400
Rate of income=moneyt
The annual expense is 700*12, which is 8400
A soft drink manufacturer produces 3408 cans in an 8-hour day. Cans are packaged 24 to a case. How many cases are produced each week? each month? (Assume one week is 40 hours, and one month is four weeks.)
Answers
3408 / 24 = 142 cases per 8 hour day
40 hours / 8 = 5 days
142 * 5 = 710 cases per week
710 * 4 = 2840 cases per month
gavin bakes 70 cookies in a hour. how many cookies can he bake in 4 hours?
A.350
B.240
C.280
D.210
Answers
To find out how many cookies Gavin can bake in 4 hours, we multiply the number of cookies he makes in one hour (70) by 4, resulting in 280 cookies.
Explanation:If Gavin bakes 70 cookies in one hour, to calculate the number of cookies he can bake in 4 hours, we simply need to multiply the amount he can bake in one hour by 4. The calculation is as follows:
Multiply the number of cookies baked in one hour (70) by the number of hours (4).70 cookies/hour × 4 hours = 280 cookies.
Therefore, the correct answer is C. 280 cookies.
A rectangular park has an area of 2/3 square mile.The length of the park is 2 2/3 the width of the park.What is the width of the park?
Answers
We know that area of a rectangle is length times width:
A = lw
The length is 2 2/3 the width, so
l = 2 2/3w
We will change this to an improper fraction; multiply the denominator by the whole number and add the numerator:
l = 8/3w
Using this for l in the area formula, we have:
A = (8/3w)(w) = 8/3w²
2/3 = 8/3w²
Divide both sides by 8/3:
2/3÷8/3 = 8/3w²÷8/3
2/3×3/8 = w²
2/8 = w²
0.25 = w²
Take the square root of both sides:
√0.25 = √w²
0.5 = w
3/7b, 5/3c, 11/21bc The LCD is
Answers
a triangle with three acute angles and no congruent sides
Answers
Hope this helped! ♡
pls find 5he area of each rectangle thxs
Answers
The area is the product of length and width.
7×10=70
Divide 180° in a ratio of 4:5:9
Answers
[tex]\bf \cfrac{180}{4+5+9}\implies 10\qquad \qquad \qquad \qquad \qquad \stackrel{4\cdot 10}{40}~:~\stackrel{5\cdot 10}{50}~:~\stackrel{9\cdot 10}{90}[/tex]
(I will give brainliest. Please answer quickly)
Leia cuts congruent triangular patches with an area of 21 square centimeters from a rectangular piece of fabric that is 14 centimeters long and 6 centimeters wide. How many of the patches can Leia cut from 31 pieces of the fabric?
Answers
The first step to solve this problem is to find the area of the rectangular piece of fabric.
A of triangle = bh/2
A = (14 cm) (6 cm) /2
A = 84 cm^2 / 2
A = 42 cm
And since there are 31 pieces of the fabric, the total area of all the pieces of fabric is:
31 pieces of fabric x 42 square centimeters per piece = 1,302 square centimeters
To computer how many congruent triangular patches can be cut, you have to divide the total area of the fabric pieces with the area of the congruent triangle:
1,302 square centimeters / 21 square centimeters = 62
Therefore, Leia can cut 62 patches.
You open a checking account. You are paid 3% interest on the average daily balance, but are charged a $4 monthly charge. Assuming that interest is paid monthly (regardless of the number of days in the month), calculate the average balance you must maintain to offset the $4 monthly charge.
Answers
You must maintain an average balance of $1,600.
4 = P*0.03*(1/12)
P = 48/.03 = 1600
Your average daily balance must be $1600 to offset the fee.