A person is standing 50 meters away from a vertical pole. If the angle of elevat

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Question: A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, what is the height of the pole?

Options:

25 m
30 m
35 m
40 m

Correct Answer: 30 m

Solution:

Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.

A person is standing 50 meters away from a vertical pole. If the angle of elevat

Practice Questions

A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, what is the height of the pole?

25 m
30 m
35 m
40 m

Questions & Step-by-Step Solutions

A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, what is the height of the pole?

Step 1: Understand the problem. You have a pole and a person standing 50 meters away from it.
Step 2: The angle of elevation to the top of the pole is given as 60 degrees.
Step 3: Recall the tangent function in a right triangle: tan(angle) = opposite side / adjacent side.
Step 4: In this case, the opposite side is the height of the pole, and the adjacent side is the distance from the person to the pole (50 meters).
Step 5: Write the equation using the tangent of the angle: tan(60°) = height / 50.
Step 6: Find the value of tan(60°). It is equal to √3.
Step 7: Substitute tan(60°) into the equation: √3 = height / 50.
Step 8: To find the height, multiply both sides of the equation by 50: height = 50 * √3.
Step 9: Calculate the height: height ≈ 50 * 1.732 (since √3 ≈ 1.732).
Step 10: The final height of the pole is approximately 86.6 meters.

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

A person is standing 50 meters away from a vertical pole. If the angle of elevat

What’s inside this PDF?

A person is standing 50 meters away from a vertical pole. If the angle of elevat

Practice Questions

Questions & Step-by-Step Solutions

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