# If sides A and B of a triangle have lengths of 5 and 9 respectively, and the angle between them is #(pi)/4#, then what is the area of the triangle?

##### 1 Answer

Mar 19, 2016

#### Explanation:

Given a triangle , where 2 sides and the angle between them are known, then the area of the triangle can be calculated using

Area =

# 1/2 ABsintheta # where A and B are the 2 sides and

#theta # , the angle between themhere A = 5 , B = 8 and

# theta = pi/4 # hence area

# = 1/2xx5xx9xxsin(pi/4) = 45/(2sqrt2) # where the exact value of

# sin(pi/4) = 1/sqrt2 # Rationalising the denominator of the fraction, to obtain

area

# = 45/(2sqrt2) = (45sqrt2)/4 ≈ 15.91" square units " #