A person is standing 25 meters away from a vertical pole. If the angle of elevat
Practice Questions
Q1
A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 53 degrees, what is the height of the pole?
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Questions & Step-by-Step Solutions
A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 53 degrees, what is the height of the pole?
Correct Answer: 20.68 meters
Step 1: Understand the problem. You have a person standing 25 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 person looks up to the top of the pole is 53 degrees.
Step 3: 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).
Step 4: Set up the equation. The height of the pole can be found using the formula: Height = distance * tan(angle).
Step 5: Plug in the values. Here, the distance is 25 meters and the angle is 53 degrees. So, Height = 25 * tan(53°).
Step 6: Calculate tan(53°). Using a calculator, tan(53°) is approximately 1.327.
Step 7: Multiply the distance by the tangent value. So, Height = 25 * 1.327.
Step 9: Conclusion. The height of the pole is approximately 20.68 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 the concept of angle of elevation is crucial for solving problems involving heights and distances.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the pole is the opposite side, the distance from the pole is the adjacent side, and the angle of elevation is the angle formed.
