Use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Question

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

A	=  °
B	=  °
C	=  °

Answer 1

The cosine law is a² = b² + c² - 2bc cos A. Since we know a, b, and c, we will use this to solve for A.

2bc cos A = b² + c² - a²

A = cos^-1 (b² + c² - a² )/2bc

A = cos^-1 (b² + c² - a² )/2bc = cos^-1(3² + 9² - 7² )/2*3*9

A = cos^-1(41/54)

A = 40.60°

B = cos^-1 (a² + c² - b² )/2ac = cos^-1(7² + 9² - 3² )/2*7*9

B = cos^-1(121/126)

B = 16.20°

We also could have derived B using the sin law

a/sin A = b/sin B

sin B = b sin A/a

B = sin^-1 (3 * sin(40.60°)/7) = sin^-1(.2789) = 16.2°

C = 180° - 40.60° - 16.20° = 123.2°

As a check, C = cos^-1 (3² + 7² - 9²)/2*3*7

C = cos^-1(-23/42)

C = 123.2°

Answer 2

Hi Natalie G.,

If I'm not mistaken, that's c^2 = a^2 + b^2 - 2abcosC (1) and likewise for the other sides. So:

b^2 = a^2 + c^2 - 2accosB (2) and

a^2 = b^2 + c^2 - 2bccosA (3). You have 3 equations with 3 unknowns. But DO NOT try to solve by substitution! You will NOT get to an easy solution, because you will mix the variables up and you ONLY have one other identity to use: A + B + C = 360 . So you would NOT be able to solve.

But just solve each of these equations on its own. That gives you hard values for cosA, cosB, and cosC, which your calculator will solve for you (as cos^-1 function).

-- Cheers, -- Mr. d.