Question

use the information given in the figure to find the length eh.
if applicable, round your answer to the nearest whole number.
the lengths on the figure are not drawn accurately.

Explanation:

Step1: Apply Pythagorean theorem to find \(FH\)

In right - triangle \(FGH\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = FG = 65\) and \(b=HG = 63\). Let \(a = FH\). Then \(FH=\sqrt{FG^{2}-HG^{2}}\).

$$FH=\sqrt{65^{2}-63^{2}}=\sqrt{(65 + 63)(65 - 63)}=\sqrt{128\times2}=\sqrt{256}=16$$

Step2: Apply Pythagorean theorem to find \(EH\)

In right - triangle \(EFH\), by the Pythagorean theorem \(EH=\sqrt{EF^{2}-FH^{2}}\), where \(EF = 34\) and \(FH = 16\).

$$EH=\sqrt{34^{2}-16^{2}}=\sqrt{(34 + 16)(34 - 16)}=\sqrt{50\times18}=\sqrt{900}=30$$

Answer:

\(30\)