A Person Is Standing Exactly 36 Ft From A Telephone Pole. There Is A 30 ∘ 30^{\circ} 3 0 ∘ Angle Of Elevation From The Ground To The Top Of The Pole.What Is The Height Of The Pole?A. 12 Ft B. 12 3 12 \sqrt{3} 12 3 Ft C. 18 Ft D. $18

Mar 11, 2025 by ADMIN 238 views

**A Person Standing 36 ft from a Telephone Pole: Calculating the Height of the Pole**

Introduction

In this article, we will explore a problem involving trigonometry and right triangles. A person is standing 36 ft away from a telephone pole, and there is a $30^{\circ}$ angle of elevation from the ground to the top of the pole. We need to calculate the height of the pole using this information.

Understanding the Problem

To solve this problem, we need to understand the concept of trigonometry and right triangles. A right triangle is a triangle with one angle that is $90^{\circ}$ . In this case, the angle of elevation is $30^{\circ}$ , which means that the triangle formed by the pole, the ground, and the line of sight is a right triangle.

Visualizing the Problem

Let's visualize the problem by drawing a diagram. We can draw a right triangle with the pole as the vertical leg, the ground as the horizontal leg, and the line of sight as the hypotenuse. The angle of elevation is $30^{\circ}$ , and the distance from the person to the pole is 36 ft.

  +---------------+
  |               |
  |  36 ft       |
  |               |
  +---------------+
  |               |
  |  30°         |
  |               |
  +---------------+
  |               |
  |  height      |
  |               |
  +---------------+

Using Trigonometry to Solve the Problem

Now that we have visualized the problem, we can use trigonometry to solve it. We can use the sine function to relate the angle of elevation, the height of the pole, and the distance from the person to the pole.

The sine function is defined as:

\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}

In this case, the opposite side is the height of the pole, and the hypotenuse is the distance from the person to the pole. We can plug in the values we know into the sine function:

\sin(30^{\circ}) = \frac{\text{height}}{36 \text{ ft}}

We can simplify the sine function by using the fact that $\sin(30^{\circ}) = \frac{1}{2}$ :

\frac{1}{2} = \frac{\text{height}}{36 \text{ ft}}

Now we can solve for the height of the pole:

\text{height} = \frac{1}{2} \times 36 \text{ ft}

\text{height} = 18 \text{ ft}

Conclusion

In this article, we used trigonometry to calculate the height of a telephone pole. We visualized the problem by drawing a diagram and used the sine function to relate the angle of elevation, the height of the pole, and the distance from the person to the pole. We found that the height of the pole is 18 ft.

Discussion

This problem is a classic example of a trigonometry problem involving right triangles. The sine function is a powerful tool for solving problems involving right triangles. We can use the sine function to relate the angle of elevation, the height of the pole, and the distance from the person to the pole.

Answer

The correct answer is C. 18 ft.

Additional Resources

For more information on trigonometry and right triangles, please see the following resources:

Khan Academy: Trigonometry
Mathway: Trigonometry
Wolfram Alpha: Trigonometry

References

"Trigonometry" by Michael Corral
"Geometry: Seeing, Doing, Understanding" by Harold R. Jacobs

License

Introduction

In our previous article, we explored a problem involving trigonometry and right triangles. A person is standing 36 ft away from a telephone pole, and there is a $30^{\circ}$ angle of elevation from the ground to the top of the pole. We calculated the height of the pole to be 18 ft. In this article, we will answer some frequently asked questions related to this problem.

Q: What is the angle of elevation?

A: The angle of elevation is the angle between the ground and the line of sight to the top of the pole. In this case, the angle of elevation is $30^{\circ}$ .

Q: What is the distance from the person to the pole?

A: The distance from the person to the pole is 36 ft.

Q: What is the height of the pole?

A: The height of the pole is 18 ft.

Q: How did you calculate the height of the pole?

A: We used the sine function to relate the angle of elevation, the height of the pole, and the distance from the person to the pole. We simplified the sine function and solved for the height of the pole.

Q: What is the sine function?

A: The sine function is a mathematical function that relates the angle of a right triangle to the ratio of the length of the opposite side to the length of the hypotenuse.

Q: What is the opposite side in this problem?

A: The opposite side is the height of the pole.

Q: What is the hypotenuse in this problem?

A: The hypotenuse is the distance from the person to the pole, which is 36 ft.

Q: Can you explain the concept of a right triangle?

A: A right triangle is a triangle with one angle that is $90^{\circ}$ . In this case, the angle of elevation is $30^{\circ}$ , which means that the triangle formed by the pole, the ground, and the line of sight is a right triangle.

Q: What is the importance of trigonometry in real-life situations?

A: Trigonometry is used in many real-life situations, such as navigation, physics, engineering, and architecture. It is used to calculate distances, heights, and angles in various fields.

Q: Can you provide more examples of trigonometry problems?

A: Yes, here are a few examples:

A person is standing 24 ft away from a building, and there is a $45^{\circ}$ angle of elevation from the ground to the top of the building. What is the height of the building?
A ladder is leaning against a wall, and the angle of elevation is $60^{\circ}$ . If the ladder is 12 ft long, what is the height of the wall?
A person is standing 18 ft away from a tree, and there is a $30^{\circ}$ angle of elevation from the ground to the top of the tree. What is the height of the tree?

Conclusion

In this article, we answered some frequently asked questions related to the problem of a person standing 36 ft away from a telephone pole. We explained the concept of a right triangle, the sine function, and the importance of trigonometry in real-life situations. We also provided more examples of trigonometry problems.