Hi someone please help me and thanks have a great day.Hi someone please help me and thanks have a great day.Hi someone please help me and thanks have a great day.Given EFG shown…

Question

asked Jun 24, 2023 140k views

1 Answer

Thinkerbelle · Answer 1 · 2023-06-28T01:27:46+0000

Answers:

m∠G = 59.49

m∠E = 30.51

Step-by-step explanation:

To know the measure of the angles we will use the trigonometric function sine. So, sin G can be calculated as:

$\sin G=\frac{Opposite\text{ side}}{Hypotenuse}$

Where the opposite side of ∠G is FE and the hypotenuse is GE, so replacing the values, we get:

$\begin{gathered} \sin G=(FE)/(GE) \\ \sin G=(56)/(65) \end{gathered}$

So, using the inverse function of sine, we get that the measure of angle G is:

$\begin{gathered} \sin G=0.86 \\ G=\sin ^(-1)(0.86) \\ G=59.49 \end{gathered}$

In the same way, the sine of angle E is equal to:

$\begin{gathered} \sin E=\frac{\text{ Opposite side}}{Hypotenuse} \\ \sin E=(GF)/(GE) \\ \sin E=(33)/(65) \end{gathered}$

So, solving for E, we get:

$\begin{gathered} \sin E=0.51 \\ E=\sin ^(-1)(0.51) \\ E=30.51 \end{gathered}$

Therefore, the answers are:

m∠G = 59.49

m∠E = 30.51