Question

what is the length of side a? triangle image with hypotenuse 15, base 9, right angle, side a vertical select the best answer

Explanation:

Step1: Identify the triangle type

The triangle is a right triangle (has a right angle). We can use the Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Here, hypotenuse \(c = 15\), one leg \(b = 9\), and we need to find \(a\).

Step2: Apply the Pythagorean theorem

Rearrange the formula to solve for \(a\): \(a=\sqrt{c^{2}-b^{2}}\). Substitute \(c = 15\) and \(b = 9\) into the formula: \(a=\sqrt{15^{2}-9^{2}}=\sqrt{225 - 81}=\sqrt{144}\).

Step3: Calculate the square root

\(\sqrt{144}=12\).

Answer:

12