10. The angle of depression of a car from an air balloon basket is 40^circ . The balloon is directly over a water tower that is 5 Km from the car.Find the altitude of the balloon.

To find the altitude of the balloon, we can use trigonometry. Let's denote the altitude of the balloon as \( h \).<br /><br />Given:<br />- Angle of depression: \( 40^{\circ} \)<br />- Distance from the car to the water tower: 5 km<br /><br />In a right triangle, the tangent of an angle is the ratio of the opposite side (altitude) to the adjacent side (distance). Therefore, we can use the tangent function:<br /><br />\[ \tan(40^{\circ}) = \frac{h}{5} \]<br /><br />Now, solve for \( h \):<br /><br />\[ h = 5 \times \tan(40^{\circ}) \]<br /><br />Using a calculator to find the tangent of \( 40^{\circ} \):<br /><br />\[ \tan(40^{\circ}) \approx 0.8391 \]<br /><br />So,<br /><br />\[ h \approx 5 \times 0.8391 \approx 4.1955 \]<br /><br />Therefore, the altitude of the balloon is approximately 4.1955 kilometers.