Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if b = 1.5 kilometers and c = 7.8 kilometers, what is a? if necessary, round to the nearest tenth.
a = kilometers

Explanation:

Step1: Apply Pythagorean theorem

According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, we can rewrite it to find $a$ as $a = \sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

Substitute $b = 1.5$ and $c = 7.8$ into the formula: $a=\sqrt{7.8^{2}-1.5^{2}}=\sqrt{(7.8 + 1.5)(7.8 - 1.5)}=\sqrt{9.3\times6.3}=\sqrt{58.59}$.

Step3: Calculate and round

$\sqrt{58.59}\approx7.654$, rounding to the nearest tenth gives $a\approx7.7$.

Answer:

$7.7$