A person is standing 20 meters away from a flagpole. If the angle of elevation t

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Question: A person is standing 20 meters away from a flagpole. If the angle of elevation to the top of the flagpole is 30 degrees, what is the height of the flagpole?

Options:

10√3 meters
20 meters
15 meters
5√3 meters

Correct Answer: 10√3 meters

Solution:

Using the tangent function, tan(30) = height / 20. Therefore, height = 20 * tan(30) = 20 * (1/√3) = 10√3 meters.

A person is standing 20 meters away from a flagpole. If the angle of elevation t

Practice Questions

A person is standing 20 meters away from a flagpole. If the angle of elevation to the top of the flagpole is 30 degrees, what is the height of the flagpole?

10√3 meters
20 meters
15 meters
5√3 meters

Questions & Step-by-Step Solutions

A person is standing 20 meters away from a flagpole. If the angle of elevation to the top of the flagpole is 30 degrees, what is the height of the flagpole?

Step 1: Understand the problem. You have a flagpole and a person standing 20 meters away from it.
Step 2: Identify the angle of elevation. The angle from the person's line of sight to the top of the flagpole is 30 degrees.
Step 3: Visualize the situation. Imagine a right triangle where one side is the height of the flagpole, the other side is the distance from the person to the flagpole (20 meters), and the angle is 30 degrees.
Step 4: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the flagpole) divided by the adjacent side (distance to the flagpole). So, tan(30 degrees) = height / 20.
Step 5: Rearrange the equation to find the height. Multiply both sides by 20: height = 20 * tan(30 degrees).
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 7: Substitute the value of tan(30 degrees) into the equation: height = 20 * (1/√3).
Step 8: Simplify the equation: height = 20/√3. To make it easier, multiply the numerator and denominator by √3: height = (20√3)/3.
Step 9: If you want a decimal approximation, you can calculate it, but the exact height is (20√3)/3 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the flagpole and the distance from it.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the flagpole, the ground, and the line of sight.

A person is standing 20 meters away from a flagpole. If the angle of elevation t

What’s inside this PDF?

A person is standing 20 meters away from a flagpole. If the angle of elevation t

Practice Questions

Questions & Step-by-Step Solutions

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