Question

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right triangle abc has side lengths ab=8, bc=15, and ac=17. a second right triangle, abc, has side lengths of 34, 30, and 16. first, find the ratio of the side opposite ∠c to the hypotenuse of triangle abc. then, use this ratio to identify the side length opposite point c on the second right triangle. (1 point)
the length of the side opposite c is
units

Explanation:

Step1: Identify hypotenuse of △ABC

In right triangle ABC, the hypotenuse is the longest side, so $AC=17$.

Step2: Find side opposite ∠C

The side opposite ∠C is AB, so $AB=8$.

Step3: Calculate the ratio

Ratio = $\frac{\text{side opposite } \angle C}{\text{hypotenuse}} = \frac{8}{17}$

Step4: Identify hypotenuse of △A'B'C'

The longest side of △A'B'C' is 34, so this is the hypotenuse.

Step5: Find side opposite ∠C'

Multiply the ratio by the hypotenuse of △A'B'C': $\frac{8}{17} \times 34 = 16$

Answer:

16