Question

For a right triangle that has legs a and b and hypotenuse c, find the lengt h of the side not given here a-1 c= square root of 3.

Answer 1

Use the Pythagorean theorem:
$c^2=a^2+b^2$
We have:
$a=1;\ c=\sqrt3$
Substitute:
$1^2+b^2=(\sqrt3)^2\\\\1+b^2=3\ \ \ |-1\\\\b^2=2\to b=\sqrt2$
We calculate the area of the triangle by two methods:
$A_\Delta=\dfrac{ab}{2}\ and\ A_\Delta=\dfrac{ch}{2}$

$\dfrac{h\sqrt3}{2}=\dfrac{1\sqrt2}{2}\ \ \ \ |\cdot2\\\\h\sqrt3=\sqrt2\ \ \ |\cdot\sqrt3\\\\3h=\sqrt6\ \ \ |:3\\\\h=\dfrac{\sqrt6}{3}$