RS = 20ST = 48TR = 52The side lengths of right triangle RST are given. Triangle RST is similar to triangle UVW, where S corresponds to V and T corresponds to W. What is the value of tan W ?
Correct answer: B. 5/12
- A. 5/13
- B. 5/12
- C. 12/13
- D. 12/5
Explanation
Choice B is correct. Given that the triangles RST and UVW are similar, angle T corresponds to angle W. In triangle RST, angle S is the right angle, making TR the hypotenuse. The side RS is opposite to angle T, and ST is adjacent to angle T. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Therefore, tan T = RS/ST = 20/48 = 5/12. Since angle T is equal to angle W, it follows that tan W = tan T = 5/12.Choices A and C are incorrect because they represent the sine and cosine of angle W, respectively, which are not relevant for finding the tangent. Choice D is incorrect as it represents the reciprocal of the tangent, which is cotangent.
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