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

1 Answer
Aug 18, 2017

Answer:

"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#.