A person is standing 30 m away from the base of a tree. If the angle of elevatio
Practice Questions
Q1
A person is standing 30 m away from the base of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?
15 m
20 m
25 m
30 m
Questions & Step-by-Step Solutions
A person is standing 30 m away from the base of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?
Correct Answer: 25 m
Step 1: Understand the problem. A person is standing 30 meters away from a tree and looking up at the top of the tree, forming an angle of 60 degrees with the ground.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the tree, the other side is the distance from the person to the tree (30 m), and the angle between the ground and the line of sight to the top of the tree is 60 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the tree) divided by the adjacent side (distance from the tree). So, tan(60°) = height / 30.
Step 4: Find the value of tan(60°). The value of tan(60°) is √3.
Step 5: Set up the equation. Now we have √3 = height / 30.
Step 6: Solve for height. Multiply both sides by 30 to isolate height: height = 30 * √3.
Step 7: Calculate the height. The height of the tree is approximately 30 * 1.732 (since √3 ≈ 1.732), which equals about 51.96 m.
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 properties of right triangles is essential, as the scenario describes a right triangle formed by the height of the tree, the distance from the tree, and the line of sight.
