# A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2 and the angle between sides B and C is pi/12. If side B has a length of 26, what is the area of the triangle?

Feb 17, 2018

${A}_{t} = \left(\frac{1}{2}\right) b h = \textcolor{g r e e n}{90.5668}$

#### Explanation:

$\hat{A} = \frac{\pi}{12} , \hat{C} = \frac{\pi}{2} , b = 26$

$\hat{B} = \pi - \left(\frac{\pi}{2} - \frac{\pi}{12}\right) = \frac{5 \pi}{12}$

It’s a right triangle. Hence, area ${A}_{t} = \left(\frac{1}{2}\right) a \cdot b$

To find side a

$\frac{a}{\sin} A = \frac{b}{\sin} B$

$a = \frac{26 \cdot \sin \left(\frac{\pi}{12}\right)}{\sin} \left(\frac{5 \pi}{12}\right) = 6.9667$

${A}_{t} = \left(\frac{1}{2}\right) \cdot 6.9667 \cdot 26 = \textcolor{g r e e n}{90.5668}$