<PRE><B>Question 210445</B>
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</PRE>