Question: A person is standing 30 meters away from a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?
A person is standing 30 meters away from a tree. If the angle of elevation to th
Practice Questions
Q1
A person is standing 30 meters away from a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?
30√3
20√3
10√3
40√3
Questions & Step-by-Step Solutions
A person is standing 30 meters away from 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: 30√3 meters
Step 1: Understand the problem. You 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: 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 person to the tree). So, tan(60 degrees) = height / 30 meters.
Step 4: Rearrange the formula to find the height. Multiply both sides by 30 meters: height = 30 * tan(60 degrees).
Step 5: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 6: Substitute the value of tan(60 degrees) into the equation: height = 30 * √3.
Step 7: Write the final answer. The height of the tree is 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 – The scenario can be visualized as a right triangle where the height of the tree is the opposite side, the distance from the tree is the adjacent side, and the angle of elevation is given.
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