A triangle has sides A,B, and C. If the angle between sides A and B is (5pi)/85π8, the angle between sides B and C is pi/4π4, and the length of B is 19, what is the area of the triangle?

1 Answer
Roella W.
Jan 14, 2016

Area =1/2*19*32.44 ~~308.13=12⋅19⋅32.44≈308.13

Explanation:

Sketch
The area of a triangle =1/b*h=1b⋅h where b = b=base and h=h=height

In this case tan((5pi)/8) =h/xtan(5π8)=hx and tan(pi/4) = h/ytan(π4)=hy where

x+y = B =19x+y=B=19
y=19-xy=19−x

So xtan((5pi)/8) =ytan(pi/4)xtan(5π8)=ytan(π4)
xtan((5pi)/8) = (19-x)tan(pi/4)xtan(5π8)=(19−x)tan(π4)
x(tan((5pi)/8) +tan(pi/4)) = 19tan(pi/4)x(tan(5π8)+tan(π4))=19tan(π4)

:.x = 19tan(pi/4)/(tan((5pi)/8)+tan(pi/4))

h = (19tan(pi/4)/(tan((5pi)/8)+tan(pi/4)))tan((5pi)/8)
~~(19*1*2.414)/(2.414+1)
~~32.44

Area =1/2*19*32.44 ~~308.13

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