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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?

 Feb 26, 2019
 #1
avatar+4325 
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What does, "13 the length of the corresponding side," mean?
 

 Feb 27, 2019
 #2
avatar+4325 
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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
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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
 #3
avatar+194 
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hmmmm indecision

 Feb 27, 2019
 #4
avatar+194 
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nah you wrong, i dont think so

 Feb 27, 2019
 #6
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Bigbrotherdude, you are given the angle measures in triangle ABC. The only tricky part is figuring out the side lengths of triangle ABC. Once you figure them out, or at least one side length, you should be able to find what the value of SinF is. :)

Guest Feb 27, 2019
 #7
avatar+194 
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i already got the answer

 Feb 27, 2019
 #8
avatar+194 
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.

 Feb 27, 2019

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