How do you solve the triangle given w=20, x=13, y=12?

1 Answer
Pop Quiz Whiz
Aug 18, 2017

"W," "X," and "Y," refer to the angles opposite sides "w," "x," and "y."

W = 106.1913516^o
X = 38.62483288^o
Y = 35.18381552^o

Explanation:

"W," "X," and "Y," refer to the angles opposite sides "w," "x," and "y."

Start by finding any angle using the Law of Cosines.
cos(A)=(b^2+c^2-a^2)/(2bc)
Plugging in the numbers, we get:
cos(W)=(13^2+12^2-20^2)/(2*13*12)
Therefore,
cos^(-1)((13^2+12^2-20^2)/(2*13*12))=W
Simplifying inside of the parentheses, we get:
cos^(-1)((-29)/104)=W
Therefore, the measure of angle W is about
106.1913516^o

Next, we can apply the Law of Sines.
sin(106.1913516^o)/20=sin(X)/13
Rearranging the numbers, we get:
13sin(106.1913516^o)/20=sin(X)
Therefore,
X=sin^(-1)(13sin(106.1913516^o)/20)
Therefore, the measure of angle X is about
38.62483288^o

Lastly, we can apply the truth that the sum of all interior angles in a triangle is 180^o.
180^o - 106.1913516^o - 38.62483288^o = Y
Simplifying, we find the measure of angle Y to be about:
35.18381552^o

Therefore, the measure of angle W is 106.1913516^o, the measure of angle X is 38.62483288^o, and the measure of angle Y is 35.18381552^o.

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