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

May 16, 2018

A=color(red)(4.61939766256 " square units"

#### Explanation:

Use $A r e a = \frac{1}{2} \times a \times b \times \sin C$

$A = \cancel{\textcolor{red}{\frac{1}{2}}} \times 5 \times \cancel{\textcolor{red}{2}} \times \sin \left(\frac{5 \pi}{8}\right)$

A=color(red)(4.61939766256 " sq units"

Jun 18, 2018

$\text{Area of a } \Delta , {A}_{t} = \left(\frac{1}{2}\right) a \cdot b \cdot \sin C$

"Given : a = 5, b = 2, hat C = (5pi) / 8

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

${A}_{t} = 5 \sin \left(\frac{5 \pi}{8}\right) = 4.62 \text{ sq units}$