Problemas
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.
Roztwór
Francisca
professionell · Tutor durante 6 años
4.1
(301 Votos)
Respuesta
To find the altitude of the balloon, we can use trigonometry. Let's denote the altitude of the balloon as
.Given:- Angle of depression:
- Distance from the car to the water tower: 5 kmIn 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:
Now, solve for
:
Using a calculator to find the tangent of
:
So,
Therefore, the altitude of the balloon is approximately 4.1955 kilometers.