Given
Angle = 60°
hypotenuse = 32 units.
Solving for x
Adjacent to angle 60°, is side length x, we can therefore use the cosine function to solve for x
[tex]\begin{gathered} \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \cos60\degree=\frac{x}{32} \\ x=32\cdot\cos60\degree \\ x=32\cdot0.5 \\ x=16 \end{gathered}[/tex]
Therefore x = 16.
Solving for y
The opposite to angle 60° is side length y, we can use the sine function to solve for y
[tex]\begin{gathered} \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin60\degree=\frac{y}{32} \\ y=32\cdot\sin60\degree \\ y=32\cdot\frac{\sqrt{3}}{2} \\ y=16\sqrt{3} \end{gathered}[/tex]
Therefore, y = 16√3.
