[tex]\huge\boxed{\text{$60$ units$^2$}}[/tex]
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:
[tex]\begin{aligned}a^2+b^2&=c^2\\a^2+8^2&=17^2\end{aligned}[/tex]
Subtract [tex]8^2[/tex] from both sides of the equation and evaluate the powers:
[tex]\begin{aligned}a^2&=17^2-8^2\\&=289-64\\&=225\end{aligned}[/tex]
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 [tex]225[/tex]:
[tex]a=15[/tex]
Now, we can use the formula for the area of a triangle, substituting in the known values:
[tex]\begin{aligned}A&=\dfrac{1}{2}bh\\&=\dfrac{1}{2}(8)(15)\\&=\boxed{60}\end{aligned}[/tex]
