A person is standing 20 meters away from a vertical pole. If the angle of elevat
Practice Questions
Q1
A person is standing 20 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? (2022)
20√3 meters
10√3 meters
30 meters
40 meters
Questions & Step-by-Step Solutions
A person is standing 20 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? (2022)
Step 1: Understand the problem. You have a pole and a person standing 20 meters away from it.
Step 2: Identify the angle of elevation. The angle from the person's line of sight to the top of the pole is 60 degrees.
Step 3: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the pole) divided by the adjacent side (distance from the pole).
Step 4: Write the formula. Height = distance * tan(angle). Here, distance is 20 meters and angle is 60 degrees.
Step 5: Find tan(60 degrees). The value of tan(60 degrees) is √3.
Step 6: Substitute the values into the formula. Height = 20 * tan(60 degrees) = 20 * √3.
Step 7: Calculate the height. The height of the pole is 20√3 meters.
Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to calculate the height of an object using the angle of elevation and the distance from the object.
Angle of Elevation – The angle formed between the horizontal line from the observer's eye to the object and the line of sight to the top of the object.
Right Triangle Properties – Understanding the relationship between the sides and angles in a right triangle, particularly how to apply the tangent function.
