## A right triangle has side lengths that are consecutive integers and a perimeter of 12 feet. What are the angles of the triangle?

Question

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## Answers ( )

Answer:The measures of the angles are 36.9 deg, 53.1 deg, 90 deg.

Step-by-step explanation:The lengths of the sides are the famous Pythagorean triple: 3, 4, 5.

To find the angles, we use trigonometry.

Since it’s a right angle, the longest side is the hypotenuse.

The hypotenuse has length 5.

The legs have lengths 3 and 4.

tan A = opp/adj

A = tan^(-1) opp/adj

A = tan^(-1) 4/3 = 53.1 deg

The acute angles of a right triangle are complementary.

B = 90 – A = 90 deg – 53.1 deg = 36.9 deg

Answer:

The measures of the angles are 36.9 deg, 53.1 deg, 90 deg.