The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi- storeyed building are 30 and 45, respectively. Find the height of the multi-storeyed building and the distance between the two buildings.
Answers
Answer:
let PC be the multi-storeyed building and AB be the other building.
Step-by-step explanation:
consider triangle PBD,
tan 30=PD/BD
1/√3=PD/BD
BD=PD√3
consider triangle PAC,
tan 45=PC/AC
PC=AC
PC =PD+DC
PD +DC =AC
PD +DC=BD ⇒PD+8=PD√3
8=PD√3-PD
8=PD(√3-1)
PD=8/√3-1
=8×√3+1/√3-1×√3+1
=8√3+8/3-1
=8√3+8/2
=4(√3+1)
PC =PD+DC
=4(√3+1)+8
=12+4√3 =4(3+√3)
Height of the multi-storeyed building =4(3+√3
distance between two building =4(√3+3).
CRM
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