Question

Find the area of the triangle. Round your answer to the nearest tenth, if necessary.

Answer 1

A.

57.7 in.2

B.

84.0 in.2

C.

122.5 in.2

D.

67.3 in.2

Answer 2

the first thing we are going to do is to find the length of the last side AC(let it be a number x). Apply the law of cosine then we have
17^2=x^2+8^2-2.8.x.cos58
x^2-17^2+8^2-16xcos58=0
x^2-8.5x-225=0
solve this equation x=19.8
then draw a line starting from point B and perpendicular to the line AC. It's also the height of the triangle. To find the height, we use
sin58=(height)/8
height=8*sin58=6.8
Now the area of the triangle is going to be: A=(AC*height)/2=19.8*6.8/2=67.3 in2
so D