# A right triangle has a hypotenuse = 39 cm and a side = 15 cm. What is the third side?

May 15, 2018

The third side is 36 cm long.

#### Explanation:

Consider a the side of 15 cm, b the unknown side and c the hypotenuse. Use pythagoras' theorem and plug in all your values, Solve for b.

${a}^{2} + {b}^{2} = {c}^{2}$
${b}^{2} = {c}^{2} - {a}^{2}$
${b}^{2} = {39}^{2} - {15}^{2}$
${b}^{2} = 1521 - 225$
${b}^{2} = 1296$
$b = \sqrt{1296}$
$b = 36$

May 15, 2018

36 cm

#### Explanation:

In a right triangle, we know using Pythagorean Theorem that ${a}^{2} + {b}^{2} = {c}^{2}$ where c is the hypotenuse, and a and b are the two other sides.

In this example, $c = 39$, and one of the sides (since the two sides are interchangeable, let's just assume it's a) $= 15$

Inputting this value into the equation gives us ${15}^{2} + {b}^{2} = {39}^{2}$.
Subtracting ${15}^{2}$ from each side gives us ${b}^{2} = {39}^{2} - {15}^{2}$
Solving for b gives us $b = \sqrt{{39}^{2} - {15}^{2}}$

If you have a calculator with you, you could simply input values.
If not, you could use simple multiplication and subtraction or some factoring methods.

Either way, the answer is $b = 36$, so the length of the missing side is 36 cm.