Ophelia Payne is walking to her office building which she knows is 150 ft high. The angle of elevation to the top of the building from her current location is 6°. How much further does she need to walk? Show your work and round your final answer to the nearest tenth of a foot.



To solve this problem, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle of elevation to the height of the building and the distance Ophelia needs to walk.

### Given:
- Height of the building (\( h \)) = 150 feet
- Angle of elevation (\( \theta \)) = 6°

### Objective:
We need to find the distance (\( d \)) Ophelia needs to walk.

### Trigonometric Relationship:
The tangent of an angle in a right triangle is given by:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
In this case:
\[
\tan(6^\circ) = \frac{150}{d}
\]

### Solving for \( d \):
\[
d = \frac{150}{\tan(6^\circ)}
\]

### Calculation:
First, calculate \( \tan(6^\circ) \), and then find \( d \).

\[
\tan(6^\circ) \approx 0.1051
\]
\[
d = \frac{150}{0.1051} \approx 1427.4 \text{ feet}
\]

So, Ophelia needs to walk approximately **1427.4 feet** further.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the distance change if the angle of elevation increased to 10°?
2. What is the formula for the angle of elevation if the distance is known?
3. How does the height of the building affect the distance Ophelia needs to walk?
4. What if Ophelia moved closer, making the angle of elevation 20°? How would the distance change?
5. How can we use the sine or cosine functions for similar problems?

**Tip:** When dealing with right triangles, it's useful to remember the basic trigonometric ratios: sine, cosine, and tangent. Each one relates different sides of the triangle to an angle.

Ophelia Payne is walking to her office building which she knows is 150 ft high. The angle of elevation to the top of the building from her current location is 6°. How much further does she need to walk? Show your work and round your final answer to the nearest tenth of a foot.

Learn how to calculate the distance Ophelia Payne needs to walk to reach her office building using trigonometry. The problem involves a 150 ft tall building and an angle of elevation of 6°, applying the tangent function to find the solution. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation