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 13 the length of the corresponding side of triangle ABC. What is the value of sinF?

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0.6

Explanation:

 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 

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