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?

Question

Pierre Lynch

Mathematics

10 July, 06:17

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?

+5

Answers (2)

Know the Answer?

Jaylin Bowers · Answer 1

Jaylin Bowers 10 July, 06:20

0

The final answer is 3/5 or 0.6.

Kaylah Benson · Answer 2

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, si n F = si n C. From the side lengths of triangle ABC,

si n F =

oppositeside hypotenuse = AB AC = 1220 = 35

Therefore, si n F =

35.