A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2 and the angle between sides B and C is pi/12. If side B has a length of 17, what is the area of the triangle?

1 Answer
Bdub
Mar 4, 2016

angle B =pi-(pi/2 + pi/12)=(5pi)/12,-> a/sinA = b/sinB->a/sin(pi/12) = 17/sin((5pi)/12)->a=(17 sin(pi/12))/sin((5pi)/12) =4.555...
Area triangle = 1/2(a)(b)sinC=1/2(4.555...)(17)sin(pi/2)~~38.72

Explanation:

First subtract the given angles from pi to find the third angle. In order to find the area of the triangle we need to find the measurement of one of the other two sides. So I use the law of sines to find side a and then put it into the area formula and calculate. Note I use angle C since sides a and b are in my calculation.

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