Answer:
B) 24/25
Explanation:
The sine of an angle is the ratio of the opposite side of the right triangle to the hypotenuse:
Sin = Opposite/Hypotenuse
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finding the hypotenuse
In this triangle, the side opposite the angle of interest is marked as 24. The hypotenuse is unmarked, so you need to find its value. (The answer choices suggest it is 25, but we can actually compute it using the Pythagorean theorem.)
For hypotenuse h and the sides as marked, the Pythagorean theorem tells us ...
h² = 7² +24²
h² = 49 +576 = 625
h = √625 = 25 . . . . hypotenuse of the right triangle
determining the sine
The sine ratio is the ratio of the opposite side (24) to the hypotenuse (25).
sin(θ) = 24/25
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Additional comment
The mnemonic SOH CAH TOA is intended to remind you of the relationships for each of the trig functions.