Solution:
Given a right angle triangle
The side opposite the given angle is the opposite
The side opposite the right angle is the hypotenuse (the slant side)
The side next to the given angle is the adjacent, as shown below
Given the following dimensions below
[tex]\begin{gathered} Hypotenuse=Hyp=44\text{ units} \\ Opposite=Opp=z\text{ units} \\ \theta=66.7\degree \end{gathered}[/tex]
To find the value of z, we apply SOHCAHTOA
Since the hypotenuse and opposite side lengths are given, we apply sine formula which is
[tex]\sin\theta=\frac{Opp}{Hyp}[/tex]
Substitute the values into the formula above
[tex]\sin66.7\degree=\frac{z}{44}[/tex]
Solve for z
[tex]\begin{gathered} \sin66.7\degree=\frac{z}{44} \\ Crossmultiply \\ z=44\times\sin66.7\degree \\ z=40.41164\text{ units} \\ z=40.41\text{ units \lparen nearest hundredth\rparen} \end{gathered}[/tex]
Hence, the value of z is 40.41 units (nearest hundredth)
