If a person is standing 40 meters away from a vertical pole and the angle of ele

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What’s inside this PDF?

Question: If a person is standing 40 meters away from a vertical pole and the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

Options:

20√3 meters
40√3 meters
60√3 meters
80√3 meters

Correct Answer: 20√3 meters

Solution:

Height = distance * tan(60) = 40 * √3 = 20√3 meters.

If a person is standing 40 meters away from a vertical pole and the angle of ele

Practice Questions

If a person is standing 40 meters away from a vertical pole and the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

20√3 meters
40√3 meters
60√3 meters
80√3 meters

Questions & Step-by-Step Solutions

If a person is standing 40 meters away from a vertical pole and the angle of elevation to 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 40 meters away from it.
Step 2: The angle of elevation to the top of the pole is 60 degrees. This means if you draw a line from the person's eyes to the top of the pole, it makes a 60-degree angle with the ground.
Step 3: Visualize the situation. You can imagine a right triangle where: one side is the height of the pole (which we want to find), the other side is the distance from the person to the pole (40 meters), and the angle between the ground and the line to the top of the pole is 60 degrees.
Step 4: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the pole) divided by the adjacent side (distance from the pole). So, tan(60 degrees) = height / 40 meters.
Step 5: Rearrange the formula to find the height. Height = distance * tan(60 degrees).
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 7: Substitute the values into the formula. Height = 40 * √3.
Step 8: Simplify the expression. Height = 40√3 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.

If a person is standing 40 meters away from a vertical pole and the angle of ele

What’s inside this PDF?

If a person is standing 40 meters away from a vertical pole and the angle of ele

Practice Questions

Questions & Step-by-Step Solutions

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