From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?
Practice Questions
1 question
Q1
From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?
50 m
25 m
100 m
75 m
Distance = height / tan(angle) = 50 / 1 = 50 m.
Questions & Step-by-step Solutions
1 item
Q
Q: From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, 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 line from your point on the ground and the line of sight to the top of the building.
Step 2: Recognize that the height of the building is 50 meters.
Step 3: Note that the angle of elevation is 45 degrees.
Step 4: Recall that the tangent of an angle in a right triangle is the ratio of the opposite side (height of the building) to the adjacent side (distance from the point to the base of the building).
Step 5: For a 45-degree angle, the tangent value is 1 (tan(45 degrees) = 1).
Step 6: Use the formula: Distance = height / tan(angle).
Step 7: Substitute the values into the formula: Distance = 50 meters / 1.
Step 8: Calculate the distance: Distance = 50 meters.
