A person is standing on the ground and looking at the top of a tree. If the angl
Practice Questions
Q1
A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?
20√3 meters
10√3 meters
30 meters
40 meters
Questions & Step-by-Step Solutions
A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?
Step 1: Understand the problem. You have a person looking at the top of a tree from a distance of 20 meters.
Step 2: Identify the angle of elevation. The angle at which the person looks up to the top of the tree is 60 degrees.
Step 3: Recall the relationship between the height of the tree, the distance from the tree, and the angle of elevation. This can be calculated using the tangent function.
Step 4: Write down the formula for height: Height = distance * tan(angle).
Step 5: Substitute the known values into the formula: Height = 20 * tan(60 degrees).
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 7: Multiply the distance by the value of tan(60 degrees): Height = 20 * √3.
Step 8: The height of the tree is 20√3 meters.
Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the tree and the distance from the tree.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the tree, the distance from the tree, and the line of sight.
