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Geometry and Trigonometry / Right triangles and trigonometry Difficulty: Hard

The figure presents right triangle R S T such that side R T is horizontal, vertex T is to the right of vertex R, and vertex S is above R T. Side R S is labeled 12. Side S T is labeled 5. Angle S is a right angle

In triangle RST above, point W (not shown) lies on $line segment R T$ . What is the value of $cosine of angle R S W, minus sine of angle W S T$ ?

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Explanation

The correct answer is 0. Note that no matter where point W is on $side R T$ , the sum of the measures of $angle R S W$ and $angle W S T$ is equal to the measure of $angle R S T$ , which is $90 degrees$ . Thus, $angle R S W$ and $angle W S T$ are complementary angles. Since the cosine of an angle is equal to the sine of its complementary angle, $the cosine of angle R S W, equals, the sine of angle W S T$ . Therefore, $the cosine of angle R S W, minus, the sine of angle W S T, equals 0$ .