Lesson 10.5 Geometry .

anonymousgirl05:

how do you find area using trigonometry ?

The area of a triangle is 1/2 * a * b * SinC

where a and b are sides and C is the angle between them.

Let me expand on what Melody said.......what if we only know the sides of a triangle but we don't know any of the angles??

Well, we could use the law of cosines to find any of the included angles and then use the formula that Melody gave - a two step process.

Here's another way.....it's known as Heron's (or Hero's) formula

First....add all the sides of the triangle and divide by 2.....this is known as the semi-perimeter (S)

Then, multiply S*(S-A)*(S-B)*(S-C) where A, B, C are the side lengths of the triangle

Now take the square root of the product you just obtained, and that's the area.

The beauty of this "formula" is that there's really no trig involved at all!!

Your choice, though!!

CPhill:

Let me expand on what Melody said.......what if we only know the sides of a triangle but we don't know any of the angles??

Well, we could use the law of cosines to find any of the included angles and then use the formula that Melody gave - a two step process.

Here's another way.....it's known as Heron's (or Hero's) formula

First....add all the sides of the triangle and divide by 2.....this is known as the semi-perimeter (S)

Then, multiply S*(S-A)*(S-B)*(S-C) where A, B, C are the side lengths of the triangle

Now take the square root of the product you just obtained, and that's the area.

The beauty of this "formula" is that there's really no trig involved at all!!

Your choice, though!!

I've never seen that before Chris. Looks really interesting. Can you find us a proof?

I've never seen that before Chris. Looks really interesting. Can you find us a proof? [/quote]

You can find a proof at: http://en.wikipedia.org/wiki/Heron%27s_formula

Thank you Chris and Alan.