# Unit 5: Triangle Trig Project #3

## Word Problem

Maggie is given a test. She is stuck on problem #10. It requires her to solve all the angles of the triangle with the given sides.

To solve this problem she will need to use the Law Of Cosines with given sides.

## Problem #10

• a= 4; What is angle A?
• b= 7; What is angle B?
• c= 6; What is angle C?

## Angle A

Use The Law of Cosines to find Angle A.

a^2 = b^2 + c^2 − 2(b)(c) cos(A)

4^2 = 7^2 + 6^2 − 2(7)(6) cos(A)

16 = 85 − 84 cos(A)

-85 -85

-69 = -84 cos(A)

-84 -84

.8214 = cos(A)

cos-1(.8214) = A

A = 61

## Angle B

Use The Law of Cosines to find Angle B.

b^2 = a^2 + c^2 − 2(a)(c) cos(B)

7^2 = 4^2 + 6^2 − 2(4)(6) cos(B)

49 = 52 − 48 cos(B)

-52 -52

-3 = -48 cos(B)

-48 -48

.0625 = cos(B)

cos-1(.0625) = B

B = 15

## Angle C

Use The Law of Cosines to find Angle C.

c^2 = a^2 + b^2 − 2(a)(b) cos(C)

6^2 = 4^2 + 7^2 − 2(4)(7) cos(C)

36 = 65 − 56 cos(C)

-65 -65

-29 = -56 cos(C)

-56 -56

.5179 = cos(C)

cos-1(.5179) = C

C = 103