Question

In triangle RST, RS = 6 cm, ST = 7 cm, and RT = 8 cm. What is the approximate measure of the largest angle in the triangle?

Answer 1

the approximate measure of the largest angle in the triangle is 75.5 degrees

Answer 2

The approximate measure of largest angle is 76°

Explanation:

Given in triangle RST, RS = 6 cm, ST = 7 cm, and RT = 8 cm. we have to find the measure of the largest angle in the triangle.

By theorem If one side of a triangle is longer than the another side, then the angle opposite to the longer side of triangle will be larger than the angle opposite to the shorter side.

As longest side is RT.

∴ the angle opposite to the side RT is largest i.e ∠S is largest.

By cosine law,

`cos \angleS=(RS^2+ST^2-RT^2)/(2(RS)(ST))`

⇒
`cos \angleS=(6^2+7^2-8^2)/(2(6)(7))`

⇒
`cos \angleS=(6^2+7^2-8^2)/(2(6)(7))`

⇒
`cos \angleS=(1)/(4)`

⇒
`\angleS=cos^(-1)((1)/(4))=75.5224878141 \sim76^(/circ)`

The approximate measure of largest angle is 76°