What is the area of the triangle?

Question

What is the area of triangle ABC if the measure of angle A is 50 degrees, the measure of angle B is 30 degrees, and a is one meter? Round your answer to two decimal places.

 

Please show the steps taken to get the answer.

The following choices are provided as answers:

A.) 0.21 m^2

B.) 0.32 m^2

C.) 0.50 m^2

D.) None of the above

Answer 1

First, because the sum of the angles in a triangle just equal 180 degrees,  m<C =  100 degrees.

 

Use the Law of Sines to calculate c=a (sin100/sin50)=(sin100/sin50) because a=1.

 

Now calculate x=the perpendicular height of the triangle from c to angle C. Since m<B=30, x=(1/2) a=0.5.

 

The area of the triangle is (1/2) 0.5*(sin100/sin50) = 0.32 m^2! (B)