Question

In triangle ABC, the measure of angle B is 90 degrees, BC=16, and AC=20. triangle DEF is similar to triangle ABC, where vertices D, E, and F corresponds 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?

(please show your work)

Answer 1

The third side of triangle ABC is AB. Using the Pythagorean Theorem, its length is 12.
12² + 16² = 20²

∠F is congruent to ∠C and so the sin(∠F) = sin(∠C)

The sin(∠C) = opposite/hypotenuse
= |AB| / |AC|
= 12/20
= 3/5
= 0.6

So the answer is 0.6.