Question

Find m\angle Am∠Am, angle, A.
Round to the nearest degree.

Answer 1

m∠A = 106°

Explanation:

All three sides of the triangle are given in the question.

To find the measure of included angle A between two sides we will apply cosine formula,

BC²= AB² + AC² - 2(AB)(AC)cosA

(13)² = (10)² + (6)² - 2(10)(6)cosA

169 = 100 + 36 - 120cosA

cosA =
`(-169+136)/(120)`

cosA = -0.275

A =
`\text{cos}^(-1)(-0.275)`

A = 105.96°

A ≈ 106°

Therefore, m∠A = 106° will be the answer.