To compute the value of h we use the trigonometric function sine:
[tex]\begin{gathered} \sin 22^{\circ}=\frac{h}{8\text{ km}} \\ h=8\operatorname{km}\text{ }\sin 22^{\circ} \\ h=3\operatorname{km} \end{gathered}[/tex]
The altitude is 3km. Using the formula for the area of a triangle we get:
[tex]A=\frac{bh}{2}=\frac{12\operatorname{km}\cdot3\operatorname{km}}{2}=18km^2[/tex]
The area is 18 square kilometers.
