Question

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?

Answer 1

The final answer is 3/5 or 0.6.

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, sinF=sinC. From the side lengths of triangle ABC,

sinF=

oppositesidehypotenuse=ABAC=1220=35

Therefore, sinF=

35.