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 30 degrees, what is the height of the pole?
12.5 meters
25 meters
15√3 meters
20 meters
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 30 degrees, what is the height of the pole?
Correct Answer: 12.5 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 at an angle of 30 degrees.
Step 2: Visualize the situation. 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 (25 meters), and the angle between the ground and the line of sight to the top of the pole is 30 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). So, tan(30 degrees) = height / 25 meters.
Step 4: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 5: Set up the equation. Now, we can write the equation: height = 25 * tan(30 degrees). This means height = 25 * (1/√3).
Step 6: Calculate the height. Multiply 25 by (1/√3) to find the height of the pole: height = 25/√3.
Step 7: Simplify the result. You can approximate 25/√3 to get about 12.5 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the pole to the distance from the pole and the angle of elevation.
Angle of Elevation – Understanding how the angle of elevation from a point to the top of an object can be used to calculate height.
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.
