Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if b = 8 miles and c = 9 miles, what is a? if necessary, round to the nearest tenth. a = miles

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute given values

Substitute \(b = 8\) and \(c = 9\) into the formula: \(a=\sqrt{9^{2}-8^{2}}=\sqrt{81 - 64}=\sqrt{17}\).

Step3: Calculate and round

\(\sqrt{17}\approx4.1\) (rounded to the nearest tenth).

Answer:

4.1