Unit 5: Triangle Trig Project #3

By Alissa Meza

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