In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. What is the value of sinF?

Answers

Answer 1

Answer:

sinF = 3 /5 or 0.6.

Explanation:

Triangle ABC is a right triangle with its right angle at B. Therefore, AC is the hypotenuse of right triangle ABC, and AB and BC are the legs of right triangle ABC. According to the Pythagorean theorem,

AB=√202−162=√400−256=√144=12

Since triangle DEF is similar to triangle ABC, with vertex F corresponding to vertex C, the measure of angle∠F equals the measure of angle∠C. Therefore, sinF=sinC. From the side lengths of triangle ABC,

sinF = oppositeside /hypotenuse = AB /AC = 12/ 20 = 3 /5

Related Questions

8−i / 3−2i
If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a? (Note: i=√−1)

Answers

Answer:

A = 2

Explanation:

To rewrite

8−i / 3−2i

in the standard form a+bi, you need to multiply the numerator and denominator of

8−i / 3−2i

by the conjugate, 3+2i. This equals

( 8−i 3−2i )( 3+2i 3+2i )= 24+16i−3+(−i)(2i) (32)−(2i)2

Since i2=−1, this last fraction can be reduced simplified to

24+16i−3i+2 9−(−4) = 26+13i 13

which simplifies further to 2+i. Therefore, when

8−i / 3−2i

is rewritten in the standard form a + bi, the value of a is 2.

Answer:

Explanation:

We have the expression [tex]\frac{8-i}{3-2i}[/tex]. In order to simplify this, we need to multiply the bottom and top by the denominator's conjugate. The conjugate of a complex number a + bi is just a - bi. Here, the conjugate of 3 - 2i is 3 + 2i. So:

[tex]\frac{8-i}{3-2i}*\frac{3+2i}{3+2i} =\frac{24-3i+16i+2}{9+4} =\frac{26+13i}{13} =2+i[/tex]

a is the real part of a complex number, so here, a = 2.

Hope this helps!

The salesman agrees to a purchase price of $16,000. Henry has $3,000.00 saved and will get $2,000.00 as a trade-in for his current vehicle. Henry has great credit and will finance at a 3.25% interest rate over 60 months. Using this calculator, what will Henry's monthly payment on this loan be?

Answers

Answer:

$198.88

Explanation:

The total value of vehicle that the salesman has offered and agreed = $16,000

The down payment that Henry can make at the time of purchase = $3,000

Now the trade in amount, which Henry will get by trading his old vehicle = $ 2,000

The amount that needs to be paid or converted to loan would be

= 16000 – 3000 – 2000

= 11000

Henry has to take a loan of $11000 from the Bank who is offering a loan at interest rate of 3.25%.

Interest on loan for first year be = 3.25% x 11000 = 327

Interest on loan for 2nd year be = 3.25% x 8940 = 259

Interest on loan for 3rd year be = 3.25% x 6812 = 189

Interest on loan for 4th year be = 3.25% x 4615 = 116

Interest on loan for Last year be = 3.25% x 2345 = 41

Summing them up gives total value of 932.

Now monthly payement = (11932 / 60) = 198.8

Which sentence describes a liquid ? Particles are closely packed together and vibrate back and forth. Particles are in contact with each other and do not move at all. Particles are in contact with each other and are able to slip past one another Particles are not in contact with each other and are moving every quic

Answers

Answer:

Particles are closely packed together and vibrate back and forth

Explanation:

I pretty sure that is a liquid. from what i learned.

During World War I, freedom of speech was limited through laws that stopped criticism of the government. In your opinion, why do you think the Texas government would create these laws?

Answers

Answer:

The Supreme Court decided a series of cases in 1919 that helped to define the limitations of free speech. Congress passed the Espionage Act of 1917, shortly after the United States entered into World War I. The law prohibited interference in military operations or recruitment.

Explanation:

simply because during war time there are exceptions were they can bend your right to freedom of speech its all to keep us as american citizens safe.

Answer:

Answers may vary. Students will need to critically think through the reasons for the legislature’s decisions. Possible student responses include explaining how unity was needed to help win the war, or how criticism would weaken America’s desire to do what it took to triumph.

Explanation:

It is the possible answer.

The Earth has four main seasons: winter, spring, summer, and fall. Which of the following is a cause of seasonal changes on Earth?

Answers

Answer:

The cause of it is the tilt of the earth on its axis but i don't know if you have certain options or anything like that.

Explanation:

The Earth is titled at an angle of 23.5 degrees on its axis, so sunlight reaches different parts of the planet at different times. Distance from the sun causes climate to change, which causes seasons. If the Earth is directly facing the sun, it’s most likely summer in that region.

A transcript must bear an) ___ to be considered official,

A medical immunization record
B. signature or school stamp
C. ACT score
D. SAT score

Answers

B. signature or school stamp

What are three ways orchids attract insects to spread their flowers’ pollen?

Answers

Not sure about the answers but maybe the scent of the flower the colour of the petals and the nectar produced

They depend on birds, bees or insects to spread their pollen to another orchid flower. Such plants produce a smell that attracts pollinators not normally attracted to them. Other orchids trick male flies by making themselves look like female flies.

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