1. ## A Triangle

This question is related to a vector/force question, but I just need help with finding two angles:

Given the following triangle:

and knowing that a+b = 14. How can you figure out the length of a and b?

2. Originally Posted by ty2391
This question is related to a vector/force question, but I just need help with finding two angles:

Given the following triangle:

and knowing that a+b = 14. How can you figure out the length of a and b?
Well I can clearly see a right angled triangle. So i think the answer is a = 8 and b = 6

3. Sorry, the diagram may be misleading, im trying to say that the 6 and 4 split the top into two sections. (thanks for your reply though)

Anyway, I figured it out I believe, can someone confirm that: a=54/7 and b=44/7?

4. Originally Posted by ty2391
This question is related to a vector/force question, but I just need help with finding two angles:

Given the following triangle:

and knowing that a+b = 14. How can you figure out the length of a and b?
Call the clearly vertical leg (that obviously is intended to meet the side of length 10 at a right angle) c.

Then we know that
$\displaystyle a^2 = 6^2 + c^2 = 36 + c^2$
and
$\displaystyle b^2 = 4^2 + c^2 = 16 + c^2$

Then
$\displaystyle a^2 - b^2 = 20$

But
$\displaystyle a^2 - b^2 = (a + b)(a - b)$
and we know that $\displaystyle a + b = 14$. Thus
$\displaystyle 14(a - b) = 20$

$\displaystyle a - b = \frac{10}{7}$

Thus we have the system of equations
$\displaystyle a + b = 14$

$\displaystyle a - b = \frac{10}{7}$

This has a solution of
$\displaystyle a = \frac{54}{7}$
and
$\displaystyle b = \frac{44}{7}$

(Which are at least close to Isomorphism's a = 8 and b = 6.)

-Dan