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?
Practice Questions
1 question
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
Using tan(60°) = height/30, we have √3 = height/30. Therefore, height = 30√3 = 25 m.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: Using tan(60°) = height/30, we have √3 = height/30. Therefore, height = 30√3 = 25 m.
Steps: 7
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.
