Question

Right triangle $ABC$ has side lengths $AB = 7$, $BC = 24$, and $AC = 25$. A second right triangle, $A'B'C'$, has side lengths of 50, 14, and 48. Find the ratio of the side opposite $\angle A$ to the hypotenuse of triangle $ABC$. Use this ratio to identify the location of point $A'$ in the second right triangle.AnswersThe ratio of the opposite side to the hypotenuse is 0.96, and point $A'$ is opposite the side that has length 14.The ratio of the opposite side to the hypotenuse is 0.96, and point $A'$ is opposite the side that has length 48.The ratio of the opposite side to the hypotenuse is 1.04, and point $A'$ is opposite the side that has length 48.The ratio of the opposite side to the hypotenuse is 0.28, and point $A'$ is opposite the side that has length 14.

Answer 1

Opposite ∠A is BC = 24 and the hypotenuse is AC = 25, so the ratio is 24/25 = 0.96. In the second triangle the hypotenuse is 50, and 0.96·50 = 48, so A' is opposite the side of length 48.