# A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is #(pi)/4# and the angle between B and C is # (2pi)/3#. What is the area of the triangle?

##### 1 Answer

Feb 28, 2016

area ≈ 3.623 square units

#### Explanation:

To find the area of this triangle given sides A and B , use

#" area " = 1/2 AB sintheta# where

#theta " is the angle between A and B"# The sum of the 3 angles in the triangle

# = pi #

#rArr theta = [pi - (pi/4 + (2pi)/3) ] = pi - (11pi)/12 = pi/12#

# " area " = 1/2 xx4 xx 7 xx sin(pi/12) ≈ 3.623" square units "#