Given:
Required:
To find the values of x and y.
Explanation:
The given triangle is a right angle triangle. Use the following trigonometric ratios.
[tex]\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ tan\theta=\frac{opp.}{adj.} \end{gathered}[/tex]
We have
[tex]\begin{gathered} \theta=60\degree \\ hypo.=x \\ adj.=y \\ opp.=21 \end{gathered}[/tex]
Now use the trigonometric ratio formulas:
[tex]\begin{gathered} sin60\degree=\frac{21}{x} \\ \frac{\sqrt{3}}{2}=\frac{21}{x} \\ x=\frac{21\times2}{\sqrt{3}} \\ x=\frac{42}{1.732} \\ x=24.25 \end{gathered}[/tex][tex]\begin{gathered} tan60\degree=\frac{21}{y} \\ \sqrt{3}=\frac{21}{y} \\ y=\frac{21}{\sqrt{3}} \\ y=\frac{21}{1.732} \\ y=12.12 \end{gathered}[/tex]
Final Answer:
x = 24.25
y = 12.12
