A person standing on the ground observes the top of a tree at an angle of elevat
Practice Questions
Q1
A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the tree, what is the height of the tree?
5 m
10 m
15 m
20 m
Questions & Step-by-Step Solutions
A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the tree, what is the height of the tree?
Step 1: Understand that the angle of elevation is the angle formed between the ground and the line of sight to the top of the tree.
Step 2: Note that the angle of elevation is 45 degrees.
Step 3: Recognize that the person is standing 10 meters away from the base of the tree.
Step 4: Use the tangent function, which relates the angle of elevation to the height of the tree and the distance from the tree.
Step 5: Write the formula: tan(angle) = height / distance.
Step 6: Substitute the known values into the formula: tan(45°) = height / 10.
Step 7: Know that tan(45°) equals 1.
Step 8: Set up the equation: 1 = height / 10.
Step 9: Solve for height by multiplying both sides by 10: height = 10 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 the angle of elevation relates to the height of an object and the distance from the observer.
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.
