Question

what is the length of the missing leg? if necessary, round to the nearest tenth.
(there is a right triangle with one leg labeled 9 mi, hypotenuse labeled 10 mi, and the other leg labeled ( a ) (in miles))

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of length \(a\) and \(b\) and hypotenuse of length \(c\), \(a^{2}+b^{2}=c^{2}\). Let the hypotenuse \(c = 10\) mi and one leg \(b=9\) mi, and we want to find the other leg \(a\).

Step2: Rearrange the Pythagorean theorem

We can solve for \(a\) by rearranging the formula: \(a^{2}=c^{2}-b^{2}\)

Step3: Substitute the values

Substitute \(c = 10\) and \(b = 9\) into the formula: \(a^{2}=10^{2}-9^{2}=100 - 81=19\)

Step4: Solve for \(a\)

Take the square root of both sides: \(a=\sqrt{19}\approx4.4\) (rounded to the nearest tenth)

Answer:

\(4.4\)