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 = meters

Explanation:

Step1: Write the Pythagorean theorem formula

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 64\), \(c = 80\), and we need to find \(b\). So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute the values

Substitute \(c = 80\) and \(a = 64\) into the formula \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=80^{2}-64^{2}\).
Calculate \(80^{2}=6400\) and \(64^{2}=4096\). So, \(b^{2}=6400 - 4096=2304\).

Step3: Find \(b\)

Take the square root of \(b^{2}\). Since \(b>0\) (length cannot be negative), \(b=\sqrt{2304}\). And \(\sqrt{2304}=48\).

Answer:

\(48\) meters