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=(ab)/(2)\ and\ A_\Delta=(ch)/(2)`


`(h\sqrt3)/(2)=(1\sqrt2)/(2)\ \ \ \ |\cdot2\\\\h\sqrt3=\sqrt2\ \ \ |\cdot\sqrt3\\\\3h=\sqrt6\ \ \ |:3\\\\h=(\sqrt6)/(3)`