
Homework:7.3
Question 3, 7.3.75
HW Score: 20%, 2 of 10 points
 Points: 0 of 1


Skip to Main content
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question content area top
Part 1
A​ blimp, suspended in the air at a height of 400 ​feet, lies directly over a line from a sports stadium to a planetarium. If the angle of depression from the blimp to the stadium is 36degrees and from the blimp to the planetarium is 24degrees​, find the distance between the sports stadium and the planetarium.
36 degrees
24 degrees
400 ft
Sports Stadium
Platentarium
Question content area bottom
Part 1
The distance between the sports stadium and the planetarium is 
  
enter your response here feet.
​(Round to two decimal places as​ needed.)
The distance between the sports stadium and the planetarium is(Round to two decimal places as needed.)The distance between the sports stadium and the planetarium is(Round to two decimal places as needed.)The distance between the sports stadium and the planetarium is(Round to two decimal places as needed.)The distance between the sports stadium and the planetarium is(Round to two decimal places as needed.)The distance between the sports stadium and the planetarium is(Round to two decimal places as needed.)
Get more help 


We are given a problem involving angles of depression and distances in relation to a blimp at a height of 400 feet. The task is to find the distance between the sports stadium and the planetarium. Here’s how we can solve it step by step:

### Problem Setup:
- The height of the blimp is \( h = 400 \) feet.
- The angle of depression from the blimp to the sports stadium is \( 36^\circ \).
- The angle of depression from the blimp to the planetarium is \( 24^\circ \).

We are asked to find the distance between the sports stadium and the planetarium.

### Step 1: Define distances
Let's define:
- \( d_1 \) as the horizontal distance from the blimp to the sports stadium.
- \( d_2 \) as the horizontal distance from the blimp to the planetarium.

From the geometry of the situation, the angles of depression are equal to the angles between the vertical line from the blimp and the lines from the blimp to each location (stadium or planetarium). Using these angles, we can apply the tangent function.

### Step 2: Apply the tangent function
From basic trigonometry, we know that:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
Where the opposite side is the height of the blimp (400 feet) and the adjacent side is the horizontal distance from the blimp to the stadium or planetarium.

For the stadium:
\[
\tan(36^\circ) = \frac{400}{d_1}
\]
Solving for \( d_1 \):
\[
d_1 = \frac{400}{\tan(36^\circ)}
\]

For the planetarium:
\[
\tan(24^\circ) = \frac{400}{d_2}
\]
Solving for \( d_2 \):
\[
d_2 = \frac{400}{\tan(24^\circ)}
\]

### Step 3: Find the total distance between the stadium and planetarium
The total distance between the stadium and the planetarium is the difference between \( d_2 \) and \( d_1 \):
\[
\text{Distance} = d_2 - d_1
\]

Now, let's compute this.

The distance between the sports stadium and the planetarium is approximately 347.86 feet, rounded to two decimal places.

Do you need more details or have any questions about the solution?

Here are 5 related questions to extend your understanding:
1. How does the angle of depression affect the horizontal distance calculation?
2. Can this method be used for other shapes, like hills or mountains, instead of a blimp?
3. How would the solution change if the blimp's height increased?
4. What if the angles of depression were the same for both the stadium and planetarium?
5. How can you solve this problem using other trigonometric functions, like sine or cosine?

**Tip:** Always double-check your calculator's settings to ensure it's in degrees when working with trigonometric functions involving angles in degrees.

A blimp, suspended in the air at a height of 400 feet, lies directly over a line from a sports stadium to a planetarium. If the angle of depression from the blimp to the stadium is 36 degrees and from the blimp to the planetarium is 24 degrees, find the distance between the sports stadium and the planetarium.

Solve a trigonometric problem involving a blimp at 400 feet and angles of depression to a sports stadium and planetarium. Learn how to calculate the horizontal distance between two points using the tangent function. Suitable for Grades 10-12, this problem covers key trigonometric concepts and functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation