Two boys ababu and chungwa on the same side of building are 100m apart .the building and the two boys are in straight line and angles of elevation from boys to the top of the building are30 and 20 respectfully calculate the height of building
Let's denote the height of the building as H.
From the information given, we can set up two right-angled triangles where the building is the vertical side, and the distance between the two boys is the base:
In triangle AOB:
- OA = H
- AB = 100m
- Angle AOB = 90 degrees
- Angle OAB = 30 degrees
In triangle AOC:
- OC = H
- AC = 100m
- Angle AOC = 90 degrees
- Angle OAC = 20 degrees
We can use trigonometry to relate the sides of the triangles. For triangle AOB:
tan 30 = H / 100
For triangle AOC:
tan 20 = H / 100
Solving for H in both equations:
H = 100 * tan 30
H = 100 * tan 20
H = 57.74 meters (rounded to two decimal places)
Therefore, the height of the building is approximately 57.74 meters.