Question

a triangle region has sides measuring 25, 35, 15 feet find the measure of the largest angle in the region

Answer 1

Remember that

In any triangle: The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle

so

In this problem

The largest angle is opposite the 35 units side

therefore

Applying the law of cosines

`c^2=a^2+b^2-2abcosC`

where

c=35 ft

a=25 ft

b=15 ft

C is the largest angle (angle between side a and side b)

substitute

`35^2=25^2+15^2-2(25)(15)cosC`

Solve for cosC

`cosC=(25^2+15^2-35^2)/(2(25)(15))`
`C=120^o`

The measure of the largest angle is 120 degrees