In triangle ABC, a = 3, b = 7, and angle C = 86º. Find the area of the triangle correct to the nearest tenth?

1 Answer
Apr 24, 2018

#a=3#
#b=7#
#C=86°#

Explanation:

The picture is symbolic, just a sketch
The area of a triangle is: #T=(h*b)/2#
If we draw a line from the top angle #B# perpendicular to #b#, we get a right triangle. The angle #C# is opposite to #h#:
#sin(C)=h/a => h=sin(C)*a#
#T=(h*b)/2= (sin(C)*a*b)/2= (sin(86°)*3*7)/2=11.5#

There are other methods to calculate the area of a triangle, sometime Heron's formula can be useful.