In triangle ABC, one of the trisector of angle A is a median, and the other is an altitude. If BC = 24, what is the area of triangle ABC?

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- Feb 18th 2011, 01:59 AMKalodaangle trisector?
In triangle ABC, one of the trisector of angle A is a median, and the other is an altitude. If BC = 24, what is the area of triangle ABC?

- Feb 18th 2011, 06:06 AMearboth
1. I've drawn a sketch (see attachment)

2. is an isosceles triangle and therefore the height h bisects half of .

3. In the right triangle you know about the angle :

4. According to the question .

In the right triangle you know:

5. Since you'll get:

Solve for h and subsequently calculate the area of the triangle

__Spoiler__: - Feb 23rd 2011, 06:13 PMfireballs619
I was looking over this, and am somewhat confused about step 5 the solution. I am not sure how you got the second half of that fraction. If possible, could you elaborate on that? Thanks!

- Feb 23rd 2011, 11:51 PMearboth
- Feb 24th 2011, 05:16 AMfireballs619
Oh, my apologies, as I did not realize that it was a formula. I thought you had somehow derived it from the diagram, and I could not for the life of me figure out how. Thanks for the time, though!