Choose the correct trigonometric function

Oct 13, 2025 by windailys.com 8 views

Introduction

In this article, we will explore a real-world problem that involves trigonometry. Chichi is standing 31.92 feet away from a building and looks up to the top of the building at an angle of elevation of 40°. We need to find the height of the building using trigonometric functions. This problem is a great example of how trigonometry can be applied to solve real-world problems.

Understanding the Problem

To solve this problem, we need to understand the concept of angle of elevation and how it relates to the height of the building. The angle of elevation is the angle between the horizontal and the line of sight to the top of the building. In this case, the angle of elevation is 40°.

Visualizing the Problem

Let's visualize the problem by drawing a diagram. We can draw a right-angled triangle with the building as the vertical leg, the distance from Chichi to the building as the horizontal leg, and the line of sight to the top of the building as the hypotenuse.

  +---------------+
  |               |
  |  Building    |
  |               |
  +---------------+
           |
           |
           v
  +---------------+
  |               |
  |  Chichi     |
  |               |
  +---------------+
           |
           |
           v
  +---------------+
  |               |
  |  Distance   |
  |  (31.92 ft) |
  |               |
  +---------------+

Applying Trigonometry

Now that we have a visual representation of the problem, we can apply trigonometry to find the height of the building. We can use the tangent function to relate the angle of elevation to the height of the building.

tan(40°) = opposite side (height of building) / adjacent side (distance from Chichi to building)

We can rearrange this equation to solve for the height of the building:

height of building = tan(40°) x distance from Chichi to building

Calculating the Height

Now that we have the equation, we can plug in the values to find the height of the building. We know that the distance from Chichi to the building is 31.92 feet and the angle of elevation is 40°.

height of building = tan(40°) x 31.92 ft

Using a calculator, we can find the value of tan(40°) and multiply it by 31.92 ft to find the height of the building.

tan(40°) = 0.8391
height of building = 0.8391 x 31.92 ft
height of building = 26.69 ft

Conclusion

In this article, we used trigonometry to find the height of a building. We applied the tangent function to relate the angle of elevation to the height of the building and used a calculator to find the value of tan(40°). We then multiplied this value by the distance from Chichi to the building to find the height of the building. This problem is a great example of how trigonometry can be applied to solve real-world problems.

Real-World Applications

Trigonometry has many real-world applications, including:

Surveying: Trigonometry is used in surveying to find the height of buildings, the distance between landmarks, and the angle of elevation to the top of a building.
Physics: Trigonometry is used in physics to describe the motion of objects, including the angle of elevation to the top of a projectile.
Engineering: Trigonometry is used in engineering to design buildings, bridges, and other structures, including the angle of elevation to the top of a building.

Practice Problems

Here are some practice problems to help you apply trigonometry to solve real-world problems:

A person is standing 25 feet away from a building and looks up to the top of the building at an angle of elevation of 30°. Find the height of the building.
A surveyor is measuring the distance between two landmarks. The angle of elevation to the top of the first landmark is 40° and the angle of elevation to the top of the second landmark is 50°. Find the distance between the two landmarks.
A physicist is studying the motion of a projectile. The angle of elevation to the top of the projectile is 60° and the distance from the projectile to the observer is 30 feet. Find the height of the projectile.

Conclusion

Introduction

In our previous article, we explored a real-world problem that involved trigonometry. We used the tangent function to find the height of a building. In this article, we will answer some frequently asked questions about trigonometry.

Q: What is trigonometry?

A: Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the use of trigonometric functions, such as sine, cosine, and tangent, to solve problems.

Q: What are the three main trigonometric functions?

A: The three main trigonometric functions are:

Sine (sin): The ratio of the length of the opposite side to the length of the hypotenuse.
Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse.
Tangent (tan): The ratio of the length of the opposite side to the length of the adjacent side.

Q: How do I use trigonometry to solve problems?

A: To use trigonometry to solve problems, you need to:

Identify the problem: Determine what you are trying to find, such as the height of a building or the distance between two landmarks.
Draw a diagram: Draw a diagram of the problem to help you visualize it.
Choose the correct trigonometric function: Choose the trigonometric function that is most relevant to the problem.
Plug in the values: Plug in the values you know into the equation.
Solve the equation: Solve the equation to find the answer.

Q: What are some common trigonometric identities?

A: Some common trigonometric identities include:

Pythagorean identity: sin^2(x) + cos^2(x) = 1
Quotient identity: tan(x) = sin(x) / cos(x)
Reciprocal identity: csc(x) = 1 / sin(x)
Co-function identity: sin(x) = cos(90° - x)

Q: How do I use trigonometry to solve right triangles?

A: To use trigonometry to solve right triangles, you need to:

Identify the right triangle: Identify the right triangle and the angle you are interested in.
Choose the correct trigonometric function: Choose the trigonometric function that is most relevant to the problem.
Plug in the values: Plug in the values you know into the equation.
Solve the equation: Solve the equation to find the answer.

Q: What are some real-world applications of trigonometry?

A: Some real-world applications of trigonometry include:

Surveying: Trigonometry is used in surveying to find the height of buildings, the distance between landmarks, and the angle of elevation to the top of a building.
Physics: Trigonometry is used in physics to describe the motion of objects, including the angle of elevation to the top of a projectile.
Engineering: Trigonometry is used in engineering to design buildings, bridges, and other structures, including the angle of elevation to the top of a building.

Q: How can I practice trigonometry?

A: You can practice trigonometry by:

Solving problems: Solve problems that involve trigonometry, such as finding the height of a building or the distance between two landmarks.
Using online resources: Use online resources, such as Khan Academy or Mathway, to practice trigonometry.
Taking a course: Take a course that covers trigonometry, such as a math or physics course.

Conclusion

In this article, we answered some frequently asked questions about trigonometry. We covered topics such as the definition of trigonometry, the three main trigonometric functions, and how to use trigonometry to solve problems. We also discussed some common trigonometric identities and real-world applications of trigonometry.