Question

1. what type of triangle has sides a = 8, b = 15, and c = 17?

a. acute triangle
b. scalene triangle
c. right triangle
d. isosceles triangle

Explanation:

Step1: Check Pythagorean theorem

We know that for a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Calculate \(a^{2}+b^{2}\): \(8^{2}+15^{2}=64 + 225=289\), and \(c^{2}=17^{2}=289\). Since \(8^{2}+15^{2}=17^{2}\), it satisfies the Pythagorean theorem.

Step2: Analyze triangle types

Since it satisfies the Pythagorean theorem, it is a right - triangle. Also, since \(a = 8\), \(b = 15\), and \(c = 17\) all have different lengths, it is a scalene triangle. But the most specific and key property here is that it is a right - triangle.

Answer:

c. Right triangle