Answers:
m∠G = 59.49
m∠E = 30.51
Explanation:
To know the measure of the angles we will use the trigonometric function sine. So, sin G can be calculated as:
[tex]\sin G=\frac{Opposite\text{ side}}{Hypotenuse}[/tex]
Where the opposite side of ∠G is FE and the hypotenuse is GE, so replacing the values, we get:
[tex]\begin{gathered} \sin G=\frac{FE}{GE} \\ \sin G=\frac{56}{65} \end{gathered}[/tex]
So, using the inverse function of sine, we get that the measure of angle G is:
[tex]\begin{gathered} \sin G=0.86 \\ G=\sin ^{-1}(0.86) \\ G=59.49 \end{gathered}[/tex]
In the same way, the sine of angle E is equal to:
[tex]\begin{gathered} \sin E=\frac{\text{ Opposite side}}{Hypotenuse} \\ \sin E=\frac{GF}{GE} \\ \sin E=\frac{33}{65} \end{gathered}[/tex]
So, solving for E, we get:
[tex]\begin{gathered} \sin E=0.51 \\ E=\sin ^{-1}(0.51) \\ E=30.51 \end{gathered}[/tex]
Therefore, the answers are:
m∠G = 59.49
m∠E = 30.51
