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 30 degrees, what is the height of the tree?
15√3 meters
15 meters
30 meters
45 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 30 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 at an angle of 30 degrees.
Step 2: Identify the right triangle formed by the man, the top of the tree, and the base of the tree. The distance from the man to the tree is the base of the triangle.
Step 3: The angle of elevation (30 degrees) is the angle between the line of sight to the top of the tree and the horizontal line from the man's eyes.
Step 4: Use the tangent function, which relates the angle of a right triangle to the opposite side (height of the tree) and the adjacent side (distance from the man to the tree).
Step 5: Write the formula: Height = distance * tan(angle). Here, distance = 30 meters and angle = 30 degrees.
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 7: Substitute the values into the formula: Height = 30 * (1/√3).
Step 8: Simplify the calculation: Height = 30/√3.
Step 9: To make it easier, multiply the numerator and denominator by √3: Height = (30√3)/3.
Step 10: Simplify further: Height = 10√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 the concept of angle of elevation is crucial for solving problems involving heights and distances.
