# If sides A and B of a triangle have lengths of 4 and 7 respectively, and the angle between them is (pi)/6, then what is the area of the triangle?

Mar 5, 2016

7 square units

#### Explanation:

In a triangle if 2 sides and the angle between them(included angle) are known, then the area can be calculated using the following :

area (A) = $\frac{1}{2} a b \sin \theta$

where a, b are the 2 sides and $\theta \text{ the angle between them }$

here a = 4 , b = 7 and $\theta = \frac{\pi}{6}$
substitute theses values into the formula.

$A = \frac{1}{2} \times 4 \times 7 \sin \left(\frac{\pi}{6}\right) = 7 \text{ square units }$

Mar 5, 2016

Area =$\frac{1}{2} A B \sin \theta = \frac{1}{2} \cdot 4 \cdot 7 \cdot \sin \left(\frac{\pi}{6}\right) = 7$squnit