A person is 40 meters away from a tower. If the angle of elevation to the top of

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Question: A person is 40 meters away from a tower. If the angle of elevation to the top of the tower is 30°, what is the height of the tower?

Options:

Correct Answer: 20 meters

Solution:

Using tan(30°) = height/40, height = 40 * tan(30°) = 40 * (1/√3) = 23.09 meters, approximately 20 meters.

A person is 40 meters away from a tower. If the angle of elevation to the top of the tower is 30°, what is the height of the tower?

A person is 40 meters away from a tower. If the angle of elevation to the top of the tower is 30°, what is the height of the tower?

Step 1: Understand the problem. You have a tower and a person standing 40 meters away from it. You need to find the height of the tower using the angle of elevation, which is 30°.
Step 2: Draw a right triangle. The person, the top of the tower, and the base of the tower form a right triangle. The distance from the person to the tower is the base (40 meters), and the height of the tower is the vertical side.
Step 3: Identify the angle. The angle of elevation from the person to the top of the tower is 30°.
Step 4: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the tower) divided by the adjacent side (distance from the person to the tower). So, tan(30°) = height / 40.
Step 5: Rearrange the equation to find the height. Multiply both sides by 40: height = 40 * tan(30°).
Step 6: Calculate tan(30°). The value of tan(30°) is 1/√3 (approximately 0.577).
Step 7: Substitute the value of tan(30°) into the equation: height = 40 * (1/√3).
Step 8: Calculate the height. height = 40 * (1/√3) = 40 / 1.732 = approximately 23.09 meters.
Step 9: Round the answer. The height of the tower is approximately 23.09 meters, which can be rounded to about 20 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the tower and the distance from the tower.
Angle of Elevation – Understanding how the angle of elevation from a point to the top of an object can be used to calculate height.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tower is the opposite side, the distance from the tower is the adjacent side, and the angle of elevation is the angle formed.