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.