Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if b = 6.2 miles and c = 8.6 miles, what is a? if necessary, round to the nearest tenth.
a = miles

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Substitute given values

Substitute $b = 6.2$ and $c = 8.6$ into the formula: $a=\sqrt{8.6^{2}-6.2^{2}}=\sqrt{(8.6 + 6.2)(8.6 - 6.2)}$ (using $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $8.6+6.2 = 14.8$ and $8.6 - 6.2=2.4$. Then $a=\sqrt{14.8\times2.4}=\sqrt{35.52}$.

Step3: Calculate the square - root and round

$\sqrt{35.52}\approx5.96\approx6.0$.

Answer:

$6.0$