From a point on the ground, the angle of elevation to the top of a 40 m high bui
Practice Questions
Q1
From a point on the ground, the angle of elevation to the top of a 40 m high building is 45 degrees. How far is the point from the base of the building?
40 m
20 m
30 m
50 m
Questions & Step-by-Step Solutions
From a point on the ground, the angle of elevation to the top of a 40 m high building is 45 degrees. How far is the point from the base of the building?
Step 1: Understand that the angle of elevation is the angle formed between the horizontal ground and the line of sight to the top of the building.
Step 2: Identify the height of the building, which is given as 40 meters.
Step 3: Recognize that the angle of elevation is 45 degrees.
Step 4: Use the tangent function, which relates the angle of elevation to the height of the building and the distance from the building.
Step 5: Write the formula: tan(angle) = height/distance.
Step 6: Substitute the known values into the formula: tan(45°) = height (40 m) / distance.
Step 7: Know that tan(45°) equals 1, so the equation becomes 1 = 40 m / distance.
Step 8: Rearrange the equation to find distance: distance = height / tan(45°).
Step 9: Substitute the values: distance = 40 m / 1.
Step 10: Calculate the distance: distance = 40 m.
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 on the ground.
Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.
Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric ratios.
