Question

"Calculate cos theta to two decimal places. (Use the pic attached inside!!!)

A. 0.61

B. 1.44

C. 0.72

D. 0.43

Answer 1

let teh greek symbol theta be equal to x. since the triangle is scalene, then apply law of cosine.

a2=b2 + c2 - 2cosx
let a = 7, b = 8 and c = 10

7^2 = 8^2 + 10^2 - 2(8)(10)cosx
cosx = 23/32 or 0.72
x = 44.05 degrees

the answer is letter C

Answer 2

Let
T = theta
Use the Law of Cosines to get
c^2 = a^2+b^2 - 2ab*cos(T)
7^2 = 10^2+8^2 - 2*10*8*cos(T)
49 = 164 - 160*cos(T)
-160cos(T) = 49-164
-160cos(T) = -115
cos(T) = -115/(-160)
cos(T) = 23/32
cos(T) = 0.71875 which rounds to 0.72

The final answer is C) 0.72