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geometry intermediate

Problem

In the diagram below, we have

sin ∠ R P Q = \frac{7}{25}

. What is

sin ∠ R P S

?

problem

Solution

For any angle

x

, we have

sin (18 0^{\circ} - x) = sin x

, so

sin R P S = sin (18 0^{\circ} - ∠ R P S) = sin ∠ R P Q = \frac{7}{25}

.

Final answer

\frac{7}{25}