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

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Answer 1 · 2017-01-10T18:14:35

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.

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:

$C = 180^@ -48 - 60$

$C ~~ 72^@$