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

Explanation:

From.the Pythagoras theorem,

DF² = DE² + EF²; therefore, DE²= DF²-EF².since each of the side of DEF is 1/3 of sides ABC , it implies that ,1/3 of 20 = 6.7 ( DF)and 1/3 of 16 = 5.3 (EF)

DE² = 6.7²-5.3²;

DE² = 44.89 - 28.09

DE² =16.8

Therefore taking the square root is both side to get the true value of DE

√DE² = √16.8; DE = 4.098.

there the value of sin of angle F

SinF°= 4.098/6.7; = 0.6116

Therefore F° = sin-¹0.6116; 37.7°.

SinF = 0.6116, while angle F = 37.7°

Note: the purpose of using the Pythagoras theorem is to help you find the third side of triangle DEF which is DE