A person is standing 15 meters away from a vertical pole. If the angle of elevat
Practice Questions
Q1
A person is standing 15 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?
15√3 meters
10√3 meters
20 meters
25 meters
Questions & Step-by-Step Solutions
A person is standing 15 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?
Correct Answer: 15√3 meters
Step 1: Understand the problem. You have a person standing 15 meters away from a vertical pole and looking up at the top of the pole.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the pole is 60 degrees.
Step 3: Visualize the situation. Imagine a right triangle where one side is the height of the pole, the other side is the distance from the person to the pole (15 meters), and the angle between the ground and the line of sight 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 the opposite side (height of the pole) divided by the adjacent side (distance from the pole). So, tan(60 degrees) = height / 15 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 = 15 meters * √3.
Step 8: Simplify the expression. The height of the pole is 15√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 the angle of elevation from a point to the top of an object can be used to calculate the height of that object.
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 between them.
