Question

How do you solve the triangle ABC given a=7, B=60, c=9?

Answer 1

Use the Law of Cosines to find the length of side b.
Use the Law of Sines to find A.
The sum is 180 for C.

Explanation:

Use the Law of Cosines to find the length of side b.

`b^2 = a^2 + c^2 - 2(a)(c)cos(B)`

Substitute, 7 for a, 9 for c, and 60 for B:

`b^2 = 7^2 + 9^2 - 2(7)(9)cos(60)`

`b^2 = 67`

`b = sqrt67`

Use the Law of Sines to find A.

`Sin(A)/a = sin(B)/b`

`A = sin^-1(a/bsin(B))`

Substitute, 7 for a, `sqrt67` for b, and 60 for B:

`A = sin^-1(7/sqrt67sin(60))`

`A ~~ 48^@`

The sum of the angles is equal to `180^@`:

`180^@ = A + B + C`

Solve for C:

`C = 180^@ -48 - 60`

`C ~~ 72^@`