Question

if a triangle has sides of lengths 8, 15, and 17, is it a right triangle?
a. cannot be determined
b. no
c. yes
d. sometimes

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.

Step2: Substitute values

Let \(a = 8\), \(b = 15\), \(c = 17\). Calculate \(a^{2}+b^{2}\): \(8^{2}+15^{2}=64 + 225=289\). Calculate \(c^{2}\): \(17^{2}=289\).

Step3: Compare results

Since \(8^{2}+15^{2}=17^{2}\), the triangle is a right - triangle.

Answer:

C. Yes