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

Mathematics

Taliyah Romero

28 March, 06:34

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?

+3

Answers (2)

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Wyatt Guzman · Answer 1

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.

Enrique Sanford · Answer 2

Enrique Sanford 28 March, 09:25

0

The final answer is 3/5 or 0.6.