OG详解-OG2 数学1 Q25

Choice B is correct. It’s given that right triangle  RST  is similar to triangle  UVW, where S  corresponds to V and T corresponds to W.  It’s given that the side lengths of the right triangle RST are RS = 20 , ST = 48, and TR = 52. Corresponding angles in similar triangles are equal. It follows that the measure of  angle T is equal to the measure of angle  W . The hypotenuse of a right triangle is the longest side. It follows that the hypotenuse of triangle  RST  is side  TR . The hypotenuse of a right triangle is the side opposite the right angle. Therefore, angle S  is a right angle. The adjacent side of an acute angle in a right triangle is the side closest to the angle that is not the hypotenuse. It follows that the adjacent side of angle T  is side  ST. The opposite side of an acute angle in a right triangle is the    side across from the acute angle. It follows that the opposite side of angle T is side RS . The tangent of an acute 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 =RSST​​. Substituting 20 for RS  and 48 for ST in this equation yields  tan T = 2048​​ ​​ or tan T = 5​12​.  The tangents of two acute angles with equal measures are equal.  Since the measure of angle T is equal to the measure of angle W, it follows that tan T = tan W. Substituting 5​12​ for tan T in this equation yields 5​12​ ​= tan W. Therefore, the value of tan W is 5​12​.
Choice A is incorrect. This is the value of sin W. Choice C is incorrect. This is the value of cos W. Choice D is incorrect. This is the value of 1​tanw​.