# A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is #(3pi)/8# and the angle between B and C is # (5pi)/24#. What is the area of the triangle?

##### 1 Answer

Feb 21, 2016

area ≈ 9.66 square units

#### Explanation:

The area of the triangle can be found using

#1/2ABsintheta #

where#theta " is the angle between A and B."# since the sum of the 3 angles in a triangle is

# pi# Then the angle

#theta = pi -((3pi)/8 + (5pi)/24)#

# rArr theta = pi - (7pi)/12 = (5pi)/12 #

#rArr "area " = 1/2 xx 4 xx 5 xx sin((5pi)/12) ≈ 9.66#