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:
Wikipedia
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 andb the base, and use the formula1/2bh 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.
Now for:
Now we go back to using Heron's Formula:
Here,
Two different methods, same answer!