A man is standing 12 meters away from a vertical pole. If he looks up at an angl
Practice Questions
Q1
A man is standing 12 meters away from a vertical pole. If he looks up at an angle of 30 degrees to see the top of the pole, what is the height of the pole?
6 meters
12 meters
8 meters
10 meters
Questions & Step-by-Step Solutions
A man is standing 12 meters away from a vertical pole. If he looks up at an angle of 30 degrees to see the top of the pole, what is the height of the pole?
Step 1: Understand the problem. A man is standing 12 meters away from a vertical pole and looking up at an angle of 30 degrees.
Step 2: Visualize the situation. Imagine a right triangle where the distance from the man to the pole is one side (12 meters), the height of the pole is the other side, and the line of sight to the top of the pole is the hypotenuse.
Step 3: Identify the angle. The angle of elevation from the man's eyes to the top of the pole is 30 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(30 degrees) = height / 12 meters.
Step 5: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 6: Set up the equation. Height = 12 * tan(30 degrees). Substitute the value: Height = 12 * (1/√3).
Step 7: Calculate the height. Height = 12/√3. To simplify, multiply the numerator and denominator by √3: Height = (12√3)/3 = 4√3 meters.
Step 8: Conclusion. The height of the pole is 4√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 man, the top of the pole, and the base of the pole.
