Question

Find the length of the missing side. The triangle is not drawn to scale. (image attached)thank you ! :)

Answer 1

A right triangle is given with the lengths of a leg and the hypotenuse.

It is required to find the missing side.

The Pythagorean Theorem states that in a right triangle, the relationship between the lengths of legs a and b, and the length of the hypotenuse c is:

`a^2+b^2=c^2`

Let the length of the missing side be a.

Substitute b=15 and c=17 into the equation:

`a^2+15^2=17^2`

Solve the resulting equation for a:

`\begin{gathered} a^2+15^2=17^2 \\ \text{ Evaluate the squares:} \\ \Rightarrow a^2+225=289 \\ \text{ Subtract }225\text{ from both sides:} \\ \Rightarrow a^2+225-225=289-225 \\ \Rightarrow a^2=64 \\ \text{ Take the square root of both sides:} \\ \Rightarrow√(a^2)=√(64) \\ \Rightarrow a=8 \end{gathered}`

Hence, the length of the missing side is 8.

The answer is 8.