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?

bigbrotheprodude Feb 26, 2019

#1

#2**0 **

I suppose you mean 1/3, actually. Remember that since they are similar triangles, sin C= sin F, so opposite/hypotenuse gives us 12/20=3/5

To help remember, use sohcahtoa triangle, https://www.mathsisfun.com/algebra/sohcahtoa.html.

tertre
Feb 27, 2019

#5**0 **

Tertre (calling you by your profile name), I also have my question here if you can answer it: https://web2.0calc.com/questions/need-help_68559

Thanks!

Guest Feb 27, 2019

#8**0 **

just figure out

Triangle ABC is a right triangle with its right angle at B. Therefore, AC is the hypotenuse of right triangle ABC, and AB and BC are the legs of right triangle ABC. According to the Pythagorean theorem,

AB=202−162=400−256=144=12

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, sinF=sinC. From the side lengths of triangle ABC,

sinF=oppositesidehypotenuse=ABAC=1220=35

Therefore, sinF=35.

The final answer is 35 or 0.6.

bigbrotheprodude Feb 27, 2019