# The measures of the sides of a triangle are 10, 7, and 9. How do you find the measure of the largest angle?

Jun 25, 2016

#### Answer:

The largest angle is ${76.226}^{o}$

#### Explanation:

WE use cosine law i.e. ${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$,

The largest angle will be opposite the largest side i.e. $10$.

Hence ${10}^{2} = {7}^{2} + {9}^{2} - 2 \times 7 \times 9 \times \cos C$ or

$100 = 49 + 81 - 126 \times \cos C$

Hence $\cos C = \frac{100 - 49 - 81}{- 126} = \frac{30}{126} = 0.2381$

Hence $\angle C = {76.226}^{o}$