# 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?

Mar 19, 2016

( 45sqrt2)/4 ≈ 15.91" square units "

#### 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 = $\frac{1}{2} A B \sin \theta$

where A and B are the 2 sides and $\theta$, the angle between them

here A = 5 , B = 8 and $\theta = \frac{\pi}{4}$

hence area $= \frac{1}{2} \times 5 \times 9 \times \sin \left(\frac{\pi}{4}\right) = \frac{45}{2 \sqrt{2}}$

where the exact value of $\sin \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$

Rationalising the denominator of the fraction, to obtain

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