
To find: To find the angles of the

Answer to Problem 16PPS
In triangle WXY
Angle ∠W=106∘
Angle ∠X=39∘
Angle ∠Y=35∘
Explanation of Solution
Given information:
The length three sides of triangle WXY.
XY= w = 20
WY= x = 13
WX= y= 12
Calculation:
To find the angle W, X and Y we use the cosine formula for any triangle:
x2=w2+y2−2wycosX⇒132=202+122−2×20×12×cosX⇒169=400+144−480CosX⇒169=544−480CosX⇒CosX=544−169480⇒CosX=373480⇒CosX=0.77708⇒X=cos−1(0.77708)⇒X=39.08∘⇒X=39∘
Also as we know that-
w2=x2+y2−2wycosW⇒202=132+122−2×13×12×cosW⇒400=169+144−312CosW⇒400=313−312CosW⇒CosW=313−400312⇒CosW=−87312⇒CosW=−0.2788⇒W=cos−1(−0.2788)⇒W=106.18∘⇒W=106∘
As we know
The sum of the angles of any triangle is 180∘
So
W+X+Y=180∘⇒Y=180∘−(W+X)⇒Y=180∘−(106∘+39∘)⇒Y=180∘−145∘⇒Y=35∘
In triangle WXY
Angle ∠W=106∘
Angle ∠X=39∘
Angle ∠Y=35∘
Chapter 12 Solutions
Glencoe Algebra 2 Student Edition C2014
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