Question 210445: if A= 42.2 degrees, B=13.6 degrees, and a=41.3,find the area of the triangle.round to the nearest tenth
a)138.8 sq units
b)493.8 sq units
c)327.4 sq units
d)246.9 sq units
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! if A= 42.2 degrees, B=13.6 degrees, and a=41.3,find the area of the triangle.round to the nearest tenth
a)138.8 sq units
b)493.8 sq units
c)327.4 sq units
d)246.9 sq units
The first thing we have to do is find the measure of angle C.
Angle C = 180 - (13.6 + 42.2)
Angle C = 180 - 55.8
Angle C = 124.2
We now use the law of sines to find side b.
sinA/a = SinB/b
Sin42.2/41.3 = Sin13.6/b
Cross-multiply and divide to find b.
41.3(sin13.6) = sin42.2(b)
41.3(sin13.6)/sin42.2 = b
(9.711369271)/sin42.2 = b
14.46 = b
Now that we know angle C, a and b, we can use the following formula to find the area.
A = 1/2 *ab* sinC
A = 1/2 * (41.3)(14.46) * sin124.2
A = 246.9 sq. Units...CHOICE D
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