A man is standing 10 meters away from a vertical pole. If he looks at the top of

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Question: A man is standing 10 meters away from a vertical pole. If he looks at the top of the pole at an angle of elevation of 60 degrees, what is the height of the pole?

Options:

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

Correct Answer: 10√3 meters

Solution:

Using tan(60) = height/distance, height = distance * tan(60) = 10 * √3 = 10√3 meters.

A man is standing 10 meters away from a vertical pole. If he looks at the top of

Practice Questions

A man is standing 10 meters away from a vertical pole. If he looks at the top of the pole at an angle of elevation of 60 degrees, what is the height of the pole?

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

Questions & Step-by-Step Solutions

A man is standing 10 meters away from a vertical pole. If he looks at the top of the pole at an angle of elevation of 60 degrees, what is the height of the pole?

Step 1: Understand the problem. A man is standing 10 meters away from a vertical pole and looking up at the top of the pole.
Step 2: Identify the angle of elevation. The angle at which the man looks up to the top of the pole is 60 degrees.
Step 3: Recognize the relationship between the height of the pole, the distance from the pole, and the angle of elevation. We can use the tangent function.
Step 4: Recall the tangent function. The tangent of an angle in a right triangle is equal to the opposite side (height of the pole) divided by the adjacent side (distance from the pole).
Step 5: Write the equation using the tangent function: tan(60 degrees) = height / distance.
Step 6: Substitute the known values into the equation: tan(60 degrees) = height / 10 meters.
Step 7: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 8: Rewrite the equation: √3 = height / 10.
Step 9: Solve for height by multiplying both sides by 10: height = 10 * √3.
Step 10: The height of the pole is 10√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.
Angle of Elevation – Understanding how to apply the angle of elevation in a right triangle to find the height of an object.
Right Triangle Properties – Utilizing the properties of right triangles to solve for unknown lengths using trigonometric ratios.

A man is standing 10 meters away from a vertical pole. If he looks at the top of

What’s inside this PDF?

A man is standing 10 meters away from a vertical pole. If he looks at the top of

Practice Questions

Questions & Step-by-Step Solutions

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