from the top of a hill 200m high , the angles of depression of the top and bottom of a pillar are 30 degree and 60 degree respectively. find the height of the pillar and its distance from the hill.
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Here, ∠EDF=30°=∠DFC and ∠EDA=60°=∠DAB (alternate angles)
BD=200m=height of the hill.
∴, from ΔDAB,
tan60°=DB/AB
or, √3=200/AB
or, AB=200/√3
Now, from Δ DFC,
tan30°=DC/FC
or, 1/√3=DC/(200/√3)
or, 1/√3=√3DC/200
or, DC=200/(√3×√3)
or, DC=66.6666 ≈ 66.67m
∴, Height of the pillar is 66.67m and distance from the hill is 200√3m. Ans.
BD=200m=height of the hill.
∴, from ΔDAB,
tan60°=DB/AB
or, √3=200/AB
or, AB=200/√3
Now, from Δ DFC,
tan30°=DC/FC
or, 1/√3=DC/(200/√3)
or, 1/√3=√3DC/200
or, DC=200/(√3×√3)
or, DC=66.6666 ≈ 66.67m
∴, Height of the pillar is 66.67m and distance from the hill is 200√3m. Ans.
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