Choosing the Right Trigonometric Function

Oct 13, 2025 by talynt.org 149 views

The Angle of Elevation: A Mathematical Approach to Finding the Height of a Building

In trigonometry, the angle of elevation is a fundamental concept used to determine the height of an object or a building. Given the angle of elevation and the distance from the object to the point of observation, we can use trigonometric functions to calculate the height. In this article, we will explore how to find the height of a building using the angle of elevation and the distance from its foot.

We are given that the angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is 60°. Our goal is to find the height of the building. To do this, we will use the trigonometric function that relates the angle of elevation, the distance from the foot of the building, and the height of the building.

Choosing the Right Trigonometric Function

There are three basic trigonometric functions: sine, cosine, and tangent. Each of these functions relates the angle of elevation to the height of the building and the distance from the foot of the building. To determine which function to use, we need to consider the given information.

The angle of elevation is 60°.
The distance from the foot of the building is 50 m.

Using the given information, we can see that the tangent function is the most suitable for this problem. The tangent function is defined as the ratio of the opposite side (the height of the building) to the adjacent side (the distance from the foot of the building).

Applying the Trigonometric Function

Now that we have chosen the tangent function, we can apply it to find the height of the building. The formula for the tangent function is:

tan(A) = opposite side / adjacent side

In this case, the angle A is 60°, the opposite side is the height of the building (h), and the adjacent side is the distance from the foot of the building (50 m).

Solving for the Height of the Building

Using the tangent function, we can write the equation as:

tan(60°) = h / 50

To solve for the height of the building (h), we can multiply both sides of the equation by 50:

h = 50 * tan(60°)

Calculating the Height of the Building

Now that we have the equation, we can calculate the height of the building using a calculator or a trigonometric table. The value of tan(60°) is approximately 1.732.

h = 50 * 1.732 h ≈ 86.60

Rounding to the Nearest Hundredth

Finally, we need to round the height of the building to the nearest hundredth. Rounding 86.60 to the nearest hundredth gives us 86.60.

In this article, we used the tangent function to find the height of a building given the angle of elevation and the distance from its foot. We applied the tangent function to the given information and solved for the height of the building. The result was a height of approximately 86.60 m. This demonstrates the power of trigonometry in solving real-world problems.

What other trigonometric functions can be used to find the height of a building?
How does the angle of elevation affect the height of the building?
What are some real-world applications of trigonometry in architecture and engineering?

"Trigonometry" by Michael Corral
"Mathematics for Engineers and Scientists" by Donald R. Hill

Khan Academy: Trigonometry
MIT OpenCourseWare: Trigonometry
Wolfram Alpha: Trigonometry
The Angle of Elevation: A Q&A Guide to Finding the Height of a Building

In our previous article, we explored how to find the height of a building using the angle of elevation and the distance from its foot. In this article, we will answer some frequently asked questions about the angle of elevation and trigonometry.

Q: What is the angle of elevation?

A: The angle of elevation is the angle between the horizontal plane and the line of sight to the top of an object or a building.

Q: How is the angle of elevation related to the height of a building?

A: The angle of elevation is related to the height of a building through trigonometric functions. The tangent function, in particular, is used to find the height of a building given the angle of elevation and the distance from its foot.

Q: What are the three basic trigonometric functions?

A: The three basic trigonometric functions are:

Sine (sin)
Cosine (cos)
Tangent (tan)

Q: Which trigonometric function is used to find the height of a building?

A: The tangent function is used to find the height of a building. The formula for the tangent function is:

tan(A) = opposite side / adjacent side

In this case, the opposite side is the height of the building (h), and the adjacent side is the distance from the foot of the building (d).

Q: How do I choose the right trigonometric function for a problem?

A: To choose the right trigonometric function, you need to consider the given information. If you are given the angle of elevation and the distance from the foot of the building, the tangent function is the most suitable.

Q: What are some real-world applications of trigonometry in architecture and engineering?

A: Trigonometry has many real-world applications in architecture and engineering, including:

Building design and construction
Bridge building
Tower construction
Surveying and mapping

Q: How does the angle of elevation affect the height of a building?

A: The angle of elevation affects the height of a building by changing the ratio of the opposite side (the height of the building) to the adjacent side (the distance from the foot of the building). As the angle of elevation increases, the height of the building also increases.

Q: What are some common mistakes to avoid when using trigonometry to find the height of a building?

A: Some common mistakes to avoid when using trigonometry to find the height of a building include:

Using the wrong trigonometric function
Not considering the given information
Not rounding the answer to the nearest hundredth

In this article, we answered some frequently asked questions about the angle of elevation and trigonometry. We hope that this article has provided you with a better understanding of how to use trigonometry to find the height of a building.

What other trigonometric functions can be used to find the height of a building?
How does the angle of elevation affect the height of a building?
What are some real-world applications of trigonometry in architecture and engineering?

"Trigonometry" by Michael Corral
"Mathematics for Engineers and Scientists" by Donald R. Hill

Khan Academy: Trigonometry
MIT OpenCourseWare: Trigonometry
Wolfram Alpha: Trigonometry