The length of the flag at the roof of three-storied building is 3.3 metres. From any point of road, the angles of elevation of the top and foot of the flagpost are`50^(@) and 45^(@)`. Calculate the height of three-storied building [ Let `tan 50^(@)` =1.192]

Explanation

Let AB be the building and AC be the flag post.
As per question. AC = 3.3 m,
`angleAOB = 45^(@) and angleBOC = 50^(@)`
Now, from the right-angled triangle BOC we get,
`tan50^(@) = (BC)/(OB)`
or, `1.192 = (BC)/(OB) " " or, 1.192 = (AB+AC)/(OB)`
or,` " " 1.192 = (AB+3.3)/(OB) " "` or, 1.192OB = AB + 3.3........(1)
Again from the right-angled triangle AOB we get
`tan 45^(@)=(AB)/(OB)` or, `1=(AB)/(OB) " " or "OB = AB"`
`therefore` from (1) we get, 1.192AB = AB +3.3
or, 1.192AB - AB = 3.3 or 0.192AB = 3.3
or, AB = `(3.3)/(0.192)` or, AB = 17.19 (approx.)
Hence the height of the building is 17.19 m (approx.).