From a point A, the angle of elevation of the top of a building is 45 degrees. I
Practice Questions
Q1
From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?
10 m
20 m
30 m
40 m
Questions & Step-by-Step Solutions
From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?
Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from point A and the line of sight to the top of the building.
Step 2: Note that the angle of elevation is 45 degrees.
Step 3: Recall that the height of the building is 20 meters.
Step 4: Use the tangent function, which relates the angle of elevation to the height of the building and the distance from point A to the base of the building.
Step 5: Write the formula: tan(angle) = height / distance.
Step 6: Substitute the known values into the formula: tan(45°) = 20 / distance.
Step 7: Know that tan(45°) equals 1.
Step 8: Set up the equation: 1 = 20 / distance.
Step 9: Rearrange the equation to find distance: distance = 20 / 1.
Step 10: Calculate the distance: distance = 20 meters.
Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building and the distance from the point to the base.
Angle of Elevation – Understanding the concept of angle of elevation and how it relates to right triangles.
Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric ratios.
