Question

which angle measure is always found in a right triangle? a. 120 degrees b. 90 degrees c. 60 degrees d. 45 degrees according to the pythagorean theorems converse, if a = 5, b = 12, and c = 13, what type of triangle is it? a. obtuse triangle b. right triangle c. acute triangle d. equilateral triangle

Explanation:

Step1: Recall right - triangle definition

A right - triangle has one angle equal to 90 degrees by definition.

Step2: Recall Pythagorean theorem's converse

The Pythagorean theorem's converse states that if \(a^{2}+b^{2}=c^{2}\), where \(a\), \(b\) are the legs and \(c\) is the hypotenuse of a triangle, then the triangle is a right - triangle. For \(a = 5\), \(b=12\), and \(c = 13\), we have \(a^{2}=5^{2}=25\), \(b^{2}=12^{2}=144\), and \(c^{2}=13^{2}=169\). Since \(25 + 144=169\) (i.e., \(a^{2}+b^{2}=c^{2}\)), it is a right - triangle.

Answer:

1. B. 90 degrees
2. B. Right triangle