Question: A person standing 60 meters away from a tree sees the top of the tree at an angle of elevation of 30 degrees. What is the height of the tree?
A person standing 60 meters away from a tree sees the top of the tree at an angl
Practice Questions
Q1
A person standing 60 meters away from a tree sees the top of the tree at an angle of elevation of 30 degrees. What is the height of the tree?
20√3 m
30 m
60 m
10 m
Questions & Step-by-Step Solutions
A person standing 60 meters away from a tree sees the top of the tree at an angle of elevation of 30 degrees. What is the height of the tree?
Step 1: Understand the problem. You have a tree and a person standing 60 meters away from it.
Step 2: The person sees the top of the tree at an angle of elevation of 30 degrees. This means if you draw a line from the person's eyes to the top of the tree, it makes a 30-degree angle with the ground.
Step 3: To find the height of the tree, we can use the tangent function from trigonometry. The formula is: height = distance * tan(angle).
Step 4: In this case, the distance from the person to the tree is 60 meters and the angle is 30 degrees.
Step 5: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 6: Now plug the values into the formula: height = 60 * (1/√3).
Step 7: Simplify the calculation: height = 60 / √3.
Step 8: To make it easier, multiply the numerator and denominator by √3: height = (60√3) / 3.
Step 9: Finally, simplify the fraction: height = 20√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.
Angle of Elevation – Understanding how to interpret the angle of elevation from the observer's line of sight to the top of 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 the angle formed.
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