Let us label the diagram:
Theta is the angle we are concerned with.
First, Let's find the side labeled "g". This is a right triangle on the base. Two of the sides are 3 cm and 5 cm respectively (they are the legs of the triangle). The unknown side "g" is the hypotenuse. We can use the Pythagorean Theorem to solve for "g".
The Pythagorean Theorem is:
[tex]Leg^2+\text{AnotherLeg}^2=\text{Hypotenuse}^2[/tex]
Substituting the known values, we solve for "g":
[tex]\begin{gathered} 3^2+5^2=g^2 \\ 9+25=g^2 \\ 34=g^2 \\ g=\sqrt[]{34} \end{gathered}[/tex]
Now, we have another right triangle with
One leg = MG
Another Leg = CG
Hypotenuse = MC
Given,
MG = Sqrt(34)
CG = 2
With respect to the angle Theta, we have the opposite side [CG = 2 cm] and the adjacent side [MG = Sqrt(34)]. We can use tan to find the angle THETA. Shown below:
[tex]\begin{gathered} \tan \theta=\frac{2}{\sqrt[]{34}} \\ \theta=\tan ^{-1}(\frac{2}{\sqrt[]{34}}) \\ \theta=18.93\degree \end{gathered}[/tex]
