# 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 1, what is the area of the triangle?

Feb 26, 2016

≈ 0.134 square units

#### Explanation:

Since the angle between A and B is $\frac{\pi}{2} \text{ this is a right triangle }$
with side C being the hypotenuse.

Thus area of triangle $= \frac{1}{2} A B$

Side B is known , require to find side A. Using standard trig. ratios.

$\tan \left(\frac{\pi}{12}\right) = \frac{A}{B} = \frac{A}{1} \Rightarrow A = 1 \times \tan \left(\frac{\pi}{12}\right)$

area  = 1/2AB = 1/2 xx1xxtan(pi/12) ≈ 0.134 " square units "