Question

Help with this question and include explanation

Answer 1

Remark.

My favorite. The Cos Law. Straight forward. Just use it once and it gives just one reply.

You want the angle opposite 18 feet. C is the one.

Formula

c^2 = a ^2 + b^2 - 2*a*b*Cos(C)

Givens

a = 22

b = 20

c = 18

Sub and solve

18^2 = 20^2 + 22^2 - 2*20*22*Cos(C)

18^2 = 400 + 484 - 880 * Cos(C)

324 = 400 + 484 - 880 * Cos(C)

324 = 884 - 880 * Cos(C)

-560 = - 880 * Cos(C)

-560/-880 = Cos(C)

0.6364 = Cos(C)

Now we have to go through that weird inverse thing.

2nd F

cos^-1

(0.6364

)

=

C = 50.48 degrees.

Answer 2

We need to use the Law of Cosines:

cos (C) = (a^2 + b^2 -c^2) / 2 ab

cos (C) = (22^2 + 20^2 -18^2) / (2 * 22 * 20)

cos (C) = (484 + 400 - 324) / (880)

cos (C) = 560 / 880

cos (C) = 0.6363636364

arc cosine (C) = 50.479 Degrees

Source

1728.com/trigtut2.htm

(Scroll down to All 3 sides of a triangle)