Answer:
x = 24.2
y = 12.1
Explanation:
The side with length x, the side with length 21, and the angle of 60° are related by the trigonometric function sine, so:
[tex]\begin{gathered} \sin 60=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin 60=\frac{21}{x} \end{gathered}[/tex]
Therefore, solving for x, we get:
[tex]\begin{gathered} x\cdot\sin 60=x\cdot\frac{21}{x} \\ x\cdot\sin 60=21 \\ \frac{x\cdot\sin60}{\sin60}=\frac{21}{\sin 60} \\ x=\frac{21}{\sin 60} \end{gathered}[/tex]
Then, sin 60 = 0.86, so the value of x is:
[tex]\begin{gathered} x=\frac{21}{0.86} \\ x=24.2 \end{gathered}[/tex]
In the same way, the value of y is related by the trigonometric function tangent as:
[tex]\begin{gathered} \tan 60=\frac{Opposite}{Adjacent} \\ \tan 60=\frac{21}{y} \end{gathered}[/tex]
So, solving for y, we get:
[tex]\begin{gathered} y\cdot\tan 60=y\cdot\frac{21}{y} \\ y\cdot\tan 60=21 \\ \frac{y\cdot\tan60}{\tan60}=\frac{21}{\tan 60} \\ y=\frac{21}{\tan 60} \end{gathered}[/tex]
Since tan 60 = 1.73, we get:
[tex]y=\frac{21}{1.73}=12.1[/tex]
Therefore, the answers are:
x = 24.2
y = 12.1
