A person is standing 30 meters away from the foot of a tree. If the angle of ele
Practice Questions
Q1
A person is standing 30 meters away from the foot 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√3 m
30 m
30√3 m
45 m
Questions & Step-by-Step Solutions
A person is standing 30 meters away from the foot of 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. We have a person standing 30 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 (30 meters), and the angle between the ground and the line of sight to the top of the tree is 60 degrees.
Step 3: Recall the tangent function. In a right triangle, the tangent of an angle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the tree).
Step 4: Write the formula for tangent. We can express this as tan(60°) = height / distance.
Step 5: Substitute the known values into the formula. We know the distance is 30 meters, so we have tan(60°) = height / 30.
Step 6: Solve for height. Rearranging the formula gives us height = distance * tan(60°).
Step 7: Calculate tan(60°). The value of tan(60°) is √3.
Step 8: Substitute tan(60°) back into the equation. So, height = 30 * √3.
Step 9: Calculate the height. This gives us the height of the tree as 30√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.
