FORMULABANK

Pythagoras theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides:

$a^2+b^2=c^2$

Example (Knowing both legs):

We know both legs (the shortest sides, side $a$ and side $b$) and want to find the hypotenuse (the longest side, side $c$).

We can use the formula:

$c=\sqrt{3^2+4^2}$

The equation is solved for $\mathrm{<em>c</em>}$ using the CAS tool

$c=5$

Alternatively, you can solve it as follows:

$c^2=3^2+4^2$

The equation is solved for $\mathrm{<em>c</em>}$ using the CAS tool

$c=-5\vee c=5$

Since $c$ cannot be negative, we only use the solution $c$ = 5.

Example (Knowing one leg and the hypotenuse):

We know side $a$ = 3 and side $c$ = 5. We want to find side $b$ (the other leg).

We can use the formula:

$b=\sqrt{5^2-3^2}$

The equation is solved for $b$ using the CAS tool WordMatMac:

$b=4$

Alternatively, you can solve it as follows:

$5^2=3^2+b^2$

The equation is solved for $b$ using the CAS tool WordMat:

$b=-4\vee b=4$

Since $b$ cannot be negative, we only use the solution $b$ = 4.