Question

find e.
write your answer as an integer or as a decimal rounded to the nearest tenth.
e =

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( e^{2}=EF^{2}+EG^{2}-2(EF)(EG)\cos\angle E\).
Substitute \(EF = 15\), \(EG=12\), and \(\angle E = 94^{\circ}\) into the formula:
\(e^{2}=15^{2}+12^{2}-2\times15\times12\times\cos(94^{\circ})\).

Step2: Calculate each term

First, \(15^{2}=225\), \(12^{2} = 144\).
\(\cos(94^{\circ})\approx - 0.069766\).
Then \(2\times15\times12\times\cos(94^{\circ})\approx2\times15\times12\times(- 0.069766)\approx - 25.11576\).
So \(e^{2}=225 + 144-(-25.11576)\).
\(e^{2}=225+144 + 25.11576\).
\(e^{2}=394.11576\).

Step3: Solve for \(e\)

Take the square - root of both sides: \(e=\sqrt{394.11576}\approx19.85\approx19.9\).

Answer:

\(e = 19.9\)