SOLUTION: The sides of a triangle measure 18 in, 25 in, and 36 in. To the nearest degree, what is the measure of the largest angle? (also I think this has to do with the law of cosines?)

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Question 1159265: The sides of a triangle measure 18 in, 25 in, and 36 in. To the nearest degree, what is the measure of the largest angle? (also I think this has to do with the law of cosines?)
Multiple choice:
A. 113 degrees
B. 157 degrees
C. 147 degrees
D. 159 degrees
Thank you so much :)
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

You are correct. You'll use the law of cosines to find the largest angle.

The largest angle is always opposite the longest side of any triangle. The largest side is 36 inches
a = 18
b = 25
c = 36

Let angles A,B,C be opposite sides a,b,c in that exact order. We want to find angle C as its opposite the longest side c = 36

Law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
(36)^2 = (18)^2 + (25)^2 - 2*(18)*(25)*cos(C)
1296 = 324 + 625 - 900*cos(C)
1296 = 949 - 900*cos(C)
1296 - 949 = 949 - 900*cos(C)-949
347 = -900*cos(C)
(347)/(-900) = (-900*cos(C))/(-900)
-0.385555555555556 = cos(C)
cos(C) = -0.385555555555556
arccos(cos(C)) = arccos(-0.385555555555556)
C = 112.678234158676
C = 113 after rounding to the nearest whole number


Answer: A. 113 degrees (approximately)

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.

Use the Cosine Law theorem.