# 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/6. If side B has a length of 1, what is the area of the triangle?

Apr 8, 2016

Areaof the triangle is $0.29$ units

#### Explanation:

This is a right angled triangle.The angle opposite to the side A /_A=180/6=30^0;/_C=180/2=90^0;/_B=180-(90+30)=60^0Using sine law we get$\frac{B}{\sin} B = \frac{A}{\sin} A \mathmr{and} A = 1. \left(\sin \frac{30}{\sin} 60\right) = \frac{1}{\sqrt{3}}$.So Areaof the triangle $= \frac{1}{2} \cdot b a s e \left(B\right) \cdot h e i g h t \left(A\right) = \frac{1}{2} \cdot 1 \cdot \frac{1}{\sqrt{3}} = 0.29$units[Ans]

Apr 8, 2016

Area $= \frac{1}{2 \sqrt{3}} \approx 0.29$

#### Explanation:

Using the standard trigonometric triangle for $\frac{\pi}{6}$ and then scaling it to match the given description:

The Area is $\frac{1}{2} A B$ (standard formula for a triangle).
$\textcolor{w h i t e}{\text{XX}} = \frac{1}{2} \cdot 1 \cdot \frac{1}{\sqrt{3}} = \frac{1}{2 \sqrt{3}}$