Question

topic: the pythagorean theorem
progress
question id: 119323
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
find the length of the leg a of a right triangle with leg length b = 21.5 inches and the hypotenuse c = 31.9 inches. use a calculator to estimate the square root to one decimal place.
the length of the leg a is approximately ______ inches.
the solution is

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). We need to solve for \(a\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute the given values

Given \(b = 21.5\) and \(c = 31.9\), we substitute into the formula: \(a=\sqrt{31.9^{2}-21.5^{2}}\).
First, calculate \(31.9^{2}=31.9\times31.9 = 1017.61\) and \(21.5^{2}=21.5\times21.5=462.25\).
Then \(c^{2}-b^{2}=1017.61 - 462.25=555.36\).

Step3: Calculate the square root

\(a=\sqrt{555.36}\approx23.6\) (using a calculator to estimate the square root to one - decimal place).

Answer:

\(23.6\)