Question

t.3 pythagorean theorem: find the missing leg or hypotenuse l...
what is the length of the missing leg? if necessary, round to the nearest tenth.
b = kilometers

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$, where \(c = 9\) (hypotenuse), \(a = 3\) (one leg), and \(b\) is the missing leg.

Step2: Rearrange the formula to solve for \(b\)

$$b=\sqrt{c^{2}-a^{2}}$$
Substitute \(c = 9\) and \(a = 3\) into the formula:
$$b=\sqrt{9^{2}-3^{2}}=\sqrt{81 - 9}=\sqrt{72}$$

Step3: Simplify the square root

$$\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\approx6\times1.414 = 8.5$$

Answer:

\(8.5\) kilometers