Math Help - Right Triangle

1. Right Triangle

In a right angled triangle ABC shown below, tan(angle ABC) = 1/2 and AB(hypotense)=square root of 20cm. Using simultaneous equations, find the length of AC(opposite) and BC(adjacent).

2. Originally Posted by soni
In a right angled triangle ABC shown below, tan(angle ABC) = 1/2 and AB(hypotense)=square root of 20cm. Using simultaneous equations, find the length of AC(opposite) and BC(adjacent).
You are told that $\tan{\theta} = \frac{1}{2}$.

So $\frac{O}{A} = \frac{1}{2}$.

You also have, by Pythagoras' Theorem

$O^2 + A^2 = H^2$

$O^2 + A^2 = (\sqrt{20})^2$

$O^2 + A^2 = 20$.

So solve $\frac{O}{A} = \frac{1}{2}$ and $O^2 + A^2 = 20$ simultaneously.