Question

find j.
triangle with 45°, 45°, right angle, side 17 yd, side j
write your answer in simplest radical form.
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Explanation:

Step1: Identify Triangle Type

The triangle has two 45° angles and a right angle, so it's a 45 - 45 - 90 triangle. In such triangles, the legs are equal, and the hypotenuse \( h \) is related to a leg \( l \) by \( h = l\sqrt{2} \). Here, one leg is 17 yd, and \( j \) is the hypotenuse.

Step2: Apply 45 - 45 - 90 Formula

For a 45 - 45 - 90 triangle, hypotenuse \( = \) leg \( \times\sqrt{2} \). Substituting the leg length (17 yd) into the formula: \( j = 17\sqrt{2} \).

Answer:

\( 17\sqrt{2} \)