# Triangle Problem

• Feb 3rd 2008, 04:51 PM
LordHz
Triangle Problem
The triangle ABC is a right triangle with legs BC=3 and AC=4. The two angle trisectors of angle C intersect the hypotenuse. The longer of these trisectors has length (a(√(3))+b)/c), where gcf(a,b,c)=1

Evaluate 15a-6b+32c.

Even some preliminary explanation would help great deals. I need to figure it out tonight.
• Feb 4th 2008, 01:09 AM
a tutor
Quote:

Originally Posted by LordHz
The triangle ABC is a right triangle with legs BC=3 and AC=4. The two angle trisectors of angle C intersect the hypotenuse. The longer of these trisectors has length (a(√(3))+b)/c), where gcf(a,b,c)=1

Evaluate 15a-6b+32c.

Even some preliminary explanation would help great deals. I need to figure it out tonight.

Here's an easy but tedious method:

C (0,0) A (4,0) B (0,3) Call the required length CP

equation of line throug C and P is ..... equation of line through A and B is .....

Solve simultaneously to find P then use Pythagoras to find length CP.

Or use some clever geometry.....