From a point on the ground, the angle of elevation to the top of a 75 m high bui

From a point on the ground, the angle of elevation to the top of a 75 m high building is 45 degrees. How far is the point from the building?

From a point on the ground, the angle of elevation to the top of a 75 m high building is 45 degrees. How far is the point from 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 75 meters.
Step 3: Recognize that the angle of elevation to the top of the building 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. The formula is: tan(angle) = height/distance.
Step 5: Substitute the known values into the formula: tan(45°) = height/distance, which becomes tan(45°) = 75/distance.
Step 6: Know that tan(45°) equals 1. So, the equation simplifies to: 1 = 75/distance.
Step 7: Rearrange the equation to find the distance: distance = 75/1.
Step 8: Calculate the distance, which equals 75 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 building.
Angle of Elevation – Understanding the concept of angle of elevation is crucial for visualizing the problem and applying the correct trigonometric function.