From a hot-air balloon, Nayeli measures a 35 degrees angle of depression to a landmark that’s 905 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

To find the vertical distance of the balloon above the ground, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle of depression, the horizontal distance, and the vertical distance.

Given:
- The angle of depression: \( 35^\circ \)
- The horizontal distance to the landmark: 905 feet

The tangent of an angle is the ratio of the opposite side (the vertical distance, \( h \)) to the adjacent side (the horizontal distance, 905 feet):

\[
\tan(35^\circ) = \frac{h}{905}
\]

To solve for \( h \):

\[
h = 905 \times \tan(35^\circ)
\]

Now, let's calculate this value.

The balloon's vertical distance above the ground is approximately 633.7 feet.

Would you like further details or have any questions?

Here are 5 related questions for deeper exploration:
1. What if the angle of depression was 45 degrees? How would the height change?
2. How would you find the distance if the height was known instead of the horizontal distance?
3. What is the relationship between the angle of depression and height in general?
4. How would the height change if the horizontal distance was doubled?
5. Can you derive other trigonometric functions for this scenario?

**Tip:** Always ensure your calculator is set to the correct unit (degrees or radians) based on the problem's requirements.

Solve a trigonometry problem where Nayeli measures a 35° angle of depression to a landmark 905 feet away. Learn how to calculate the balloon's vertical distance above the ground using the tangent function. Perfect for students in Grades 9-10, this problem covers angles of depression and tangent ratios.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation