Kamore stood 240 meters away from the tallest building, he had a piece of wood 40 cm long at arms length , 0.6m away from the eye.the peice of wood held vertical ,just blocked the building from my view . Using similar triangle to calculate the height of building?

Answer 1

To calculate the height of the building, we can use the concept of similar triangles.

Let x be the height of the building.

From Kamore's perspective, the piece of wood at arm's length creates a right triangle with the building. The height of the building is the opposite leg of this triangle, while the distance from Kamore to the building (240 meters) is the adjacent leg. The angle between the ground and his line of sight to the top of the building can be determined as follows:

tan θ = opposite/adjacent
tan θ = x/240
θ = arctan(x/240)

Since we know that the piece of wood is 40 cm long at arm's length and 0.6 meters away from the eye, the angle that the piece of wood creates with the eye can be calculated as follows:

tan ϕ = opposite/adjacent
tan ϕ = 0.4/0.6
ϕ = arctan(0.4/0.6)

The total angle between Kamore's line of sight and the ground can be calculated as the sum of θ and ϕ:

Total angle = θ + ϕ

Since the triangles are similar, the total angle between Kamore's line of sight and the ground is proportional to the height of the building:

Total angle / θ = Height of building / 240

Therefore, we can solve for the height of the building x using the following equation:

x = 240 * tan (Total angle / θ)