Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if a = 45 yards and c = 75 yards, what is b? if necessary, round to the nearest tenth. b = yards

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute given values

Given $a = 45$ and $c = 75$, then $b^{2}=75^{2}-45^{2}$.
\[

$$\begin{align*} b^{2}&=(75 + 45)(75 - 45)\\ &=(120)\times(30)\\ &=3600 \end{align*}$$

\]

Step3: Solve for b

$b=\sqrt{3600}=60$

Answer:

60