Question

The lengths of the triangle's sides are 5, 12, and 13. What is the measure of the angle opposite to side 13?

Answer 1

90°

Explanation:

5^2+ 12^2 = 13^2

25 + 144 = 169

The Converse Pythagorean Theorem (Egyptian triangle) states that if the length of the sides of a triangle, say a, b, and c, satisfy a^2 + b^2 = c^2, then this is a right triangle with a right angle opposite to side c.

And since 5^2 + 12^2 = 13^2 satisfies the statement a^2 + b^2 = c^2, c (which is 13) is opposite to a 90° angle.

Answer 2

90°

Explanation:

5, 12 and 13 are the sides of a right triangle ( Pythagorean triple )

13 is the measure of the hypotenuse whose opposite angle is 90°