Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if b = 8.6 yards and c = 8.8 yards, what is a? if necessary, round to the nearest tenth. a = yards

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Substitute given values

Given $b = 8.6$ and $c = 8.8$, then $a^{2}=8.8^{2}-8.6^{2}$.
\[

$$\begin{align*} a^{2}&=(8.8 + 8.6)(8.8 - 8.6)\\ a^{2}&=(17.4)\times(0.2)\\ a^{2}&=3.48 \end{align*}$$

\]

Step3: Solve for a

$a=\sqrt{3.48}\approx1.9$

Answer:

$1.9$