# A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 7, respectively. The angle between A and C is #(7pi)/24# and the angle between B and C is # (11pi)/24#. What is the area of the triangle?

##### 1 Answer

Feb 21, 2016

≈ 7.42 square units

#### Explanation:

The area can be calculated using

#1/2 ABsintheta#

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

# = pi# hence the angle between A and B

#= pi - ((7pi)/24 +(11pi)/24)#

# = pi - (18pi)/24 = (6pi)/24 = pi/4 #

#rArr " area" = 1/2xx3xx7xxsin(pi/4) ≈ 7.42" square units"#