A man is standing 30 meters away from a tree. If the angle of elevation from his
Practice Questions
Q1
A man is standing 30 meters away from a tree. If the angle of elevation from his eyes to the top of the tree is 60 degrees, what is the height of the tree?
15 meters
25 meters
30 meters
35 meters
Questions & Step-by-Step Solutions
A man is standing 30 meters away from a tree. If the angle of elevation from his eyes to the top of the tree is 60 degrees, what is the height of the tree?
Correct Answer: 51.96 meters
Step 1: Understand the problem. We have a man standing 30 meters away from a tree, and we need to find the height of the tree using the angle of elevation.
Step 2: Identify the angle of elevation. The angle given is 60 degrees.
Step 3: Recall the relationship between the height of the tree, the distance from the man to the tree, and the angle of elevation. We can use the tangent function: tan(angle) = height / distance.
Step 4: Rearrange the formula to find the height: height = distance * tan(angle).
Step 5: Substitute the known values into the formula. The distance is 30 meters and the angle is 60 degrees: height = 30 * tan(60 degrees).
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3, which is approximately 1.732.
Step 7: Multiply the distance by the value of tan(60 degrees): height = 30 * √3 = 30 * 1.732.
Step 8: Perform the multiplication: height = 51.96 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the tree to the distance from the man to the tree and the angle of elevation.
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 tree is the opposite side, the distance from the man to the tree is the adjacent side, and the angle of elevation is the angle formed.
