# 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 16, what is the area of the triangle?

##### 1 Answer

#### Explanation:

We have a triangle that looks like:

Here, we have that the angle

Since all the angles of a triangle add up to

According to the sine rule:

We have to solve for

Now there exist possibilities all around. There are a multitude of ways to solve for the area. Let's look at the **two** main ways of action.

- Take
#a# as the height of the triangle and#b# the base, and use the formula#1/2bh# to solve for the area. - Find
#c# and use Heron's Formula to solve for the area.

Just for kicks, let's do **both**!

Use **Method Number 1**:

Use **Method Number Two**:

We must find

- Use the Pythagoras' Theorem
- Use the Cosine Rule

Again, for kicks, I'm doing both.

**Sub-method Number 1**:

Now for:

**Sub-Method Number 2**

Now we go back to using Heron's Formula:

Here,

Two different methods, same answer!