A person is looking at the top of a 10-meter tall building from a distance of 20

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Question: A person is looking at the top of a 10-meter tall building from a distance of 20 meters. What is the angle of elevation?

Options:

Correct Answer: 26.57 degrees

Solution:

Using the tangent function, tan(angle) = 10 / 20. Therefore, angle = arctan(0.5) = 26.57 degrees.

A person is looking at the top of a 10-meter tall building from a distance of 20 meters. What is the angle of elevation?

A person is looking at the top of a 10-meter tall building from a distance of 20 meters. What is the angle of elevation?

Step 1: Understand the problem. We have a building that is 10 meters tall and a person standing 20 meters away from the base of the building.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building (10 meters) and the other side is the distance from the person to the building (20 meters).
Step 3: Identify the angle of elevation. This is the angle formed between the line of sight from the person to the top of the building and the horizontal line from the person to the base of the building.
Step 4: Use the tangent function. The tangent of the angle of elevation is equal to the opposite side (height of the building) divided by the adjacent side (distance from the building). So, tan(angle) = height / distance = 10 / 20.
Step 5: Simplify the fraction. 10 / 20 equals 0.5.
Step 6: Find the angle using the arctangent function. Use a calculator to find the angle: angle = arctan(0.5).
Step 7: Calculate the angle. The result is approximately 26.57 degrees.

Trigonometry – The problem involves using the tangent function to find the angle of elevation from a right triangle formed by the height of the building and the distance from the observer.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle and the angles formed, specifically how to apply the tangent function.