Mathematics: What is the area of the right triangle shown below?

Step-by-step explanation:link...

What is the area of the right triangle shown below?

payshencec21

17.01.2022

$\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:

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

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