From a point P on the ground,the angle of elevation of the top of a 10m tall building and a helicopter,hovering at some height vertically over the top of the building are 30° and 60° respectively. Based on the above information,answer the following questions. (a)Mark a figure on the basis of given information and find the angle of elevation at the top of the building,if the point P was at a distance of 10m from the building. (b)Find the height of the helicopter above the ground.
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Answer:
AC = length of building = 10 m
AD = height of helicopter hover = h
LCBA = 30°
ZDBA = 60°
In LABC,
30 AC AB =
1 √3 AC AB
1 √3 10 AB
→ AB = 10√3 m (1)
In AABD.
tan 60 = AD AB
√3 AD 10√3
- from (1)
⇒ AD = 10√√3 x √3
⇒ AD = 10 × 3
⇒ AD = 30 m
Height of helicopter hovering is 30 metres.
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