A person is standing at a distance of 40 m from a tree. If the angle of elevatio
Practice Questions
Q1
A person is standing at a distance of 40 m from a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?
20√3 m
40 m
30 m
10√3 m
Questions & Step-by-Step Solutions
A person is standing at a distance of 40 m from a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?
Step 1: Understand the problem. You have a person standing 40 meters away from a tree and looking up at the top of the tree at an angle of 60 degrees.
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 (40 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 to the tree). So, tan(60°) = height / 40 m.
Step 4: Rearrange the formula to find the height. Multiply both sides by 40 m: height = 40 m * tan(60°).
Step 5: Calculate tan(60°). The value of tan(60°) is √3 (approximately 1.732).
Step 6: Substitute the value of tan(60°) into the equation: height = 40 m * √3.
Step 7: Calculate the height. This gives you height = 40√3 m, which is approximately 69.28 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 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.
