Question

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

Answer 1

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 = sqrt1296`
`b= 36`

Answer 2

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.