A tree casts a shadow of 20 m when the angle of elevation of the sun is 45 degre
Practice Questions
Q1
A tree casts a shadow of 20 m when the angle of elevation of the sun is 45 degrees. What is the height of the tree?
10 m
20 m
30 m
40 m
Questions & Step-by-Step Solutions
A tree casts a shadow of 20 m when the angle of elevation of the sun is 45 degrees. What is the height of the tree?
Step 1: Understand that the angle of elevation is the angle between the ground and the line from the top of the tree to the sun.
Step 2: Know that when the angle of elevation is 45 degrees, the tangent of that angle (tan(45°)) is equal to 1.
Step 3: Recall the formula for tangent, which is tan(angle) = height of the tree / length of the shadow.
Step 4: Substitute the known values into the formula: tan(45°) = height / 20 m.
Step 5: Since tan(45°) = 1, we can write the equation as 1 = height / 20 m.
Step 6: To find the height, multiply both sides of the equation by 20 m: height = 1 * 20 m.
Step 7: Calculate the height: height = 20 m.
Trigonometry – The problem involves using the tangent function to relate the height of the tree to the length of its shadow based on the angle of elevation of the sun.
Angle of Elevation – Understanding how the angle of elevation affects the relationship between the height of an object and the length of its shadow.
