# If sides A and B of a triangle have lengths of 1 and 2 respectively, and the angle between them is (5pi)/8, then what is the area of the triangle?

May 3, 2018

A = 0.924 $u n i t {s}^{2}$

#### Explanation:

Remember that the equation for finding the area of a triangle is
1/2 ab sinC
So in this case the area is equal to: 1/2x1x2xsin(5$\pi$/8)
Which simply becomes sin(5$\pi$/8) (remember to have your calculator in radians mode)

May 3, 2018

color(crimson)(A_t = 0.9239 " sq units"

#### Explanation:

Formula for area of triangle = (1/2) b c sin A, knowing two sides and the included angle.

$b = 1 , c = 2 , \hat{A} = \frac{5 \pi}{8}$

$\text{Area of Triangle } {A}_{t} = \cancel{\frac{1}{2}} \cdot 1 \cdot \cancel{2} \cdot \sin \left(\frac{5 \pi}{8}\right)$

color(crimson)(A_t = sin ((5pi)/8) = 0.9239 " sq units"