A man is standing 30 meters away from a tree. If the angle of elevation of the t
Practice Questions
Q1
A man is standing 30 meters away from a tree. If the angle of elevation of the top of the tree from his eyes is 60 degrees, what is the height of the tree?
15√3 meters
30√3 meters
45 meters
30 meters
Questions & Step-by-Step Solutions
A man is standing 30 meters away from a tree. If the angle of elevation of the top of the tree from his eyes is 60 degrees, what is the height of the tree?
Step 1: Understand the problem. A man is standing 30 meters away from a tree and looking up at the top of the tree.
Step 2: Identify the angle of elevation. The angle at which the man looks up to see the top of the tree is 60 degrees.
Step 3: Visualize the situation. Imagine a right triangle where one side is the height of the tree, the other side is the distance from the man to the tree (30 meters), and the angle between the ground and the line of sight to the top of the tree 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 tree) divided by the adjacent side (distance from the man to the tree).
Step 5: Write the formula. The formula is: height = distance * tan(angle). Here, distance = 30 meters and angle = 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 = 30 * tan(60 degrees) = 30 * √3.
Step 9: Final answer. The height of the tree is 30√3 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 how the angle of elevation is used to calculate the height of an object based on a horizontal distance.
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.
