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Question 16 asks to find the distance of a car from a point directly below a helicopter that is flying at 2,400 feet. The angle of depression from the helicopter to the car is 73°.

To solve this problem, we can use trigonometry, particularly the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (the vertical distance, which is 2,400 ft) to the adjacent side (the horizontal distance we are trying to find).

Let \( x \) be the distance from the point directly below the helicopter to the car (the horizontal distance).

The formula using the tangent function is:
\[
\tan(\theta) = \frac{{\text{{opposite}}}}{{\text{{adjacent}}}} = \frac{{2400}}{{x}}
\]
where \( \theta = 73^\circ \).

We can solve for \( x \):
\[
x = \frac{{2400}}{{\tan(73^\circ)}}
\]

Using a calculator, we get:
\[
x = \frac{{2400}}{{\tan(73^\circ)}} \approx \frac{{2400}}{{3.27085}} \approx 733.74 \, \text{feet}
\]

Therefore, the distance of the car from the point directly below the helicopter is approximately **734 feet**.

Do you want more details or have any other questions?

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Here are 5 related questions for practice:

1. What if the angle of depression were 60° instead of 73°? How would that change the result?
2. How would the result change if the helicopter were flying at 3,000 feet with the same angle of depression?
3. Can you find the angle of depression if the distance of the car is 500 feet and the height of the helicopter remains 2,400 feet?
4. What trigonometric function would be used if you were given the horizontal distance and needed to find the vertical height?
5. How does the concept of the angle of depression differ from the angle of elevation?

**Tip:** In trigonometry, always visualize the right triangle formed by the horizontal and vertical distances, and label the sides carefully to choose the correct trigonometric function.

From a police helicopter flying at 2,400 ft, a stolen car is sighted at an angle of depression of 73°. Find the distance of the car (to the nearest foot) from a point directly below the helicopter.

Solve a trigonometry problem involving a helicopter flying at 2,400 ft and an angle of depression of 73°. Learn how to calculate the horizontal distance using the tangent function in a right triangle. Suitable for high school students.

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