A man standing 15.0 ft away from a light pole which is an additional 85.0 ft from a building tries to estimate the height of the building which he has lined up with the top the light-pole. Since he knows that the light-pole is 20.0 ft tall and his line of vision is 5.00 ft high, how tall is the building?
To solve this problem, we can use similar triangles. Let's assume the height of the building is "h".
1. Draw a diagram: Draw a right triangle with the man at one vertex, the light pole at another vertex, and the building at the third vertex.
2. Label the given information:
- Distance between the man and the light pole: 15.0 ft
- Distance between the light pole and the building: 85.0 ft
- Height of the light pole: 20.0 ft
- Height of the man's line of vision: 5.00 ft
3. Set up the similarity relation: The two triangles formed by the man, light pole, and building are similar. This means the ratios of corresponding sides are equal.
4. Write the similarity equation:
Height of building / Distance between man and building = Height of light pole / Distance between man and light pole
⇒ h / (15.0 ft + 85.0 ft) = 20.0 ft / 15.0 ft
5. Solve for the height of the building:
h / 100.0 ft = 4.0 / 3.0
Cross multiplying:
3.0h = 4.0 * 100.0 ft
Dividing both sides by 3.0:
h = (4.0 * 100.0 ft) / 3.0
Calculating:
h = 400.0 ft / 3.0
Simplifying:
h ≈ 133.3 ft
Therefore, the estimated height of the building is approximately 133.3 ft.
To determine the height of the building, we can use the concept of similar triangles. Let's denote the height of the building as "h".
First, let's draw a diagram to visualize the situation:
Man ------ Light Pole ------ Building
(20.0 ft) (? ft)
We have the following measurements:
- Distance between the man and the light pole: 15.0 ft
- Distance between the light pole and the building: 85.0 ft
- Height of the light pole: 20.0 ft
- Line of vision (height of the man's line of sight): 5.00 ft
Now, we can set up a proportion using the similar triangles:
(height of the building) / (distance between the man and the building) = (height of the light pole) / (distance between the man and the light pole)
h / (15.0 ft + 85.0 ft) = 20.0 ft / 15.0 ft
To simplify, let's convert all measurements to the same unit (feet) and solve the proportion:
h / 100.0 ft = 20.0 ft / 15.0 ft
Cross-multiplying, we get:
h * 15.0 ft = 20.0 ft * 100.0 ft
h = (20.0 ft * 100.0 ft) / 15.0 ft
Calculating the above expression, we find:
h = 133.33 ft
Therefore, the estimated height of the building is 133.33 ft.