Question

a right triangle has a leg of length 20 yards and a hypotenuse of length 26 yards. find the length of the other leg. provide an answer accurate to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a,b\) are legs. Let one leg \(a = 20\), hypotenuse \(c = 26\), find \(b\). Rearrange formula: \(b=\sqrt{c^2 - a^2}\).

Step2: Substitute values

\(c^2=26^2 = 676\), \(a^2 = 20^2=400\). Then \(c^2 - a^2=676 - 400 = 276\).

Step3: Calculate square root

\(b=\sqrt{276}\approx16.6\) (rounded to nearest tenth).

Answer:

\(16.6\) yards