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?
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Answer:
△ABC is a right triangle with its right angle at B.
Thus,
AC
is the hypotenuse of right triangle ABC, and
AB
and
BC
are perpendicular to each other.
By the Pythagorean theorem,
AB=
20
2
−16
2
=
400−256
=
144
=12
Given: △DEF∼△ABC
And, ∠B=∠E=90
o
Thus, sinF=sinC
From the side lengths of △ABC,
sinC=
AC
AB
=
20
12
=
5
3
Therefore, sinF=
5
3
Step-by-step explanation:
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