Question

Desperately seeking answer. Please if you don’t know don’t just comment.

Answer 1

Recall the cosine rule

$b^2=a^2+c^2-2ac \cos B$

This can be rearranged for cos B

$\cos B = \frac{a^2+c^2-b^2}{2ac}$

so $B = \cos^{-1}(\frac{90^2+50^2-55^2}{2 \times 90 \times 50})$

(I haven't worked out the number but you just put that into a calculator)

Answer 2

Remark

I always like to work from general principles. You need only remember 2 things about the cosine law.

1. An angel is found by by starting with the side opposite that angel. The side squared on the left and the angle share the same letter.

2. the other two sides do not matter how they are defined.

Step One

Define the cosine law to be used by the angle you want to solve for. Put the side opposite it on the left by itself.

b^2 = a^2 + b^2 - 2ab*cos(B) Study this carefully. Read what I've written above as you look at this equation.

Step Two

State the givens.

b = 55

a = 90

c = 50

Step Three

Substitute into the Cosine Law and solve.

55^2 = 90^2 + 50^2 - 2*90*50*Cos(B)

3025 = 8100 + 2500 - 9000*cos(B)

3025 = 10600 - 9000*cos(B)

-7575 = - 9000 * Cos(B) Divide by 9000

-7575/-9000 = - Cos(B)

8417 = cos(B)

Cos-1(0.8517) = B

32.68 = B