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The lengths of the sides of a triangle a...

The lengths of the sides of a triangle are 23, 32 , and 37 . To the nearest degree , what is the value of the largest angle ?

A

`71^(@)`

B

`83^(@)`

C

`122^(@)`

D

`128^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
The angle opposite the 37 side (call it `angleA`) is the largest angle . By the Law of Cosines , `37^2 = 23^2 + 32^2 - 2(23) (32) cos A .`
`cos A = (37^2 - 23^2 - 32^2)/(-2 (23)(32)) ~~ (-184)/(-1,472) = 0.125` .
Therefore , `A = cos^(-1) (0.125) ~~ 83^(@)`.
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