# 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 5, what is the area of the triangle?

Feb 21, 2016

$\textcolor{b l u e}{A = 3.34925}$

#### Explanation:

NOTE: Diagram drawn not to scale

Sorry for my bad drawing :D

Angles in Uppercase Letters (A, B, C)
Sides in Lowercase Letters (a, b, c)

Angle $C = \frac{\pi}{2}$

Angle $A = \frac{\pi}{12}$

to convert radian values to degrees, we simply multiply it by $\frac{180}{\pi}$

Angle $C = \frac{\pi}{2} \cdot \frac{180}{\pi} = \frac{180 \cancel{\pi}}{2 \cancel{\pi}}$

Angle $C = {90}^{o}$

Angle $A = \frac{\pi}{12} \cdot \frac{180}{\pi} = \frac{180 \cancel{\pi}}{12 \cancel{\pi}}$

Angle $A = {15}^{o}$

Side $b = 5$

we must get the value of Side $a$ to get the area of triangle,

we can use trigonometric functions to get the value of side of the triangle and apply algebraic techniques to find the value of $a$.

$\tan {15}^{o} = \frac{a}{5}$

$5 \tan {15}^{o} = a$

$a = 5 \tan {15}^{o}$

$a = 1.3397$

Since the formula for Area of Triangle is,

$A r e a = \frac{1}{2} b h$

where $b$ = base can be the side $a$, and $h =$height can be the side $b$.

Plugging All Variables,

$A r e a = \frac{1}{2} \left(1.3397\right) \left(5\right)$

$A r e a = 3.34925$