# A triangle has sides A, B, and C. The angle between sides A and B is #pi/4# and the angle between sides B and C is #pi/12#. If side B has a length of 8, what is the area of the triangle?

##### 1 Answer

6.762 (6.762395692966 to be precise)

#### Explanation:

Answer can be verified here

Please use the above link to refer the image.

Now that we have the triangle (blue coloured in the above link), let's begin.

First drop a perpendicular from vertex A to the side BC, let it meet BC at the point D.

Now, assume the length BD =

Thus, CD =

(since BC =

using trigonometry, we have:

from triangle ADB, AD=

from triangle CDB, AD=

hence we have,

solve this linear equation in x to get the value of x as 2.4136.

hence AD =

Now, looking again at the triangle ABC whose area is to be found:

We have the height (AD=1.7067), we have the base (BC=8).

Thus, area of the triangle =