In triangle abcabca, b, c, the measure of \angle b∠bangle, b is 90^\circ90 ∘ 90, degree, bc=16bc=16b, c, equals, 16, and ac=20ac=20a, c, equals, 20. triangle defdef d, e, f is similar to triangle abcabca, b, c, where vertices ddd, eee, and fff correspond to vertices aaa, bbb, and ccc, respectively, and each side of triangle def d, e, f is \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction the length of the corresponding side of triangle abcabca, b, c. what is the value of \text{sin }f sin fs, i, n, space, f

we know that

ABC is a right triangle

m∠B=90°

AC=20

BC=16

AB=?

see the attached figure to better understand the problem

Step 1

Applying the Pythagorean Theorem

Find the value of AB

Step 2

we know that

triangle ABC and triangle DEF are similar and the scale factor  is equal to (1/3)

Find the measures of the triangle DEF

Step 3

Find the value of sin F

we know that

In a right triangle, the value of the sine is equal to

in this problem

substitute

therefore

the answer is

the value of sin F is equal to

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