sat-dog

Choice B is correct. It’s given that angle Z in triangle XYZ is a right angle. Thus, side YZ is the leg opposite angle X and side XZ is the leg adjacent to angle X. The tangent of an acute angle in a right triangle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. It follows that tan X =YZ . It’s given that tan X = 3 1 5 2 and the length of side YZ is 24 units. Substitu X ti Z ng 3 1 5 2 for tan X and 24 for YZ in the equation tan X =YZ yields 3 1 5 2 = 24 . XZ XZ 35 12 =24 35 Multiplying both sides of this equation by ^XZh yields ^XZh ^ h, or 12 =840 12 =70 ^XZh . Dividing both sides of this equation by yields XZ . The length XY can be calculated using the Pythagorean theorem, which states that if a right triangle has legs with lengths of a and b and a hypotenuse with length c, 2+ 2= 2 70 24 then a b c . Substituting for a and for b in this equation yields 702+242= 2 5,476= 2 c , or c . Taking the square root of both sides of this equation !74= 74= yields c. Since the length of the hypotenuse must be positive, c. 74 Therefore, the length of XY is units. The perimeter of a triangle is the sum of 74+70+24 168 the lengths of all sides. Thus, ^ h units, or units, is the perimeter of triangle XYZ. Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This would be the perimeter, in units, for a right triangle 12 24 where the length of side YZ is units, not units. Choice D is incorrect and may result from conceptual or calculation errors.