Question

Right triangle $ABC$ has side lengths $AB = 9$, $BC = 12$, and $AC = 15$. A second right triangle, $A'B'C'$, has side lengths of 30, 24, and 18. Find the ratio of the side opposite $\angle A$ to the hypotenuse of triangle $ABC$. Then 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 0.8, and point $A'$ is opposite the side that has length 24.The ratio of the opposite side to the hypotenuse is 0.6, and point $A'$ is opposite the side that has length 18.The ratio of the opposite side to the hypotenuse is 1.25, and point $A'$ is opposite the side that has length 24.The ratio of the opposite side to the hypotenuse is 0.8, and point $A'$ is opposite the side that has length 18.

Answer 1

The side opposite ∠A is BC = 12 and the hypotenuse is AC = 15, so the ratio is 12/15 = 0.8. In the second triangle the hypotenuse is 30, and 0.8·30 = 24, so A' is opposite the side of length 24.