Question

What is the area of the right triangle shown below?

Answer 1

60

Explanation:

Answer 2

`\huge\boxed{\text{$60$ units$^2$}}`

First, we need to find the height of the triangle, as we only have the base and the hypotenuse. We can do this using the Pythagorean theorem:

`\begin{aligned}a^2+b^2&=c^2\\a^2+8^2&=17^2\end{aligned}`

Subtract
`8^2` from both sides of the equation and evaluate the powers:

`\begin{aligned}a^2&=17^2-8^2\\&=289-64\\&=225\end{aligned}`

Take the square root of both sides of the equation, keeping in mind that length cannot be negative, meaning we only need the positive root of
`225`:

`a=15`

Now, we can use the formula for the area of a triangle, substituting in the known values:

`\begin{aligned}A&=(1)/(2)bh\\&=(1)/(2)(8)(15)\\&=\boxed{60}\end{aligned}`