A man is standing on the ground and observes the top of a tree at an angle of el
Practice Questions
Q1
A man is standing on the ground and observes the top of a tree at an angle of elevation of 45 degrees. If he 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 man is standing on the ground and observes the top of a tree at an angle of elevation of 45 degrees. If he is 10 meters away from the tree, what is the height of the tree?
Step 1: Understand that the man is looking at the top of the tree at an angle of elevation of 45 degrees.
Step 2: Recognize that the distance from the man to the base of the tree is 10 meters.
Step 3: Recall the trigonometric function tangent (tan), which relates the angle of elevation to the height of the tree and the distance from the tree.
Step 4: Write the formula for tangent: tan(angle) = height / distance.
Step 5: Substitute the known values into the formula: tan(45°) = height / 10.
Step 6: Know that tan(45°) equals 1, so the equation becomes 1 = height / 10.
Step 7: Solve for height by multiplying both sides of the equation 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.
