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प्रश्न
If one looks from a tower 10 m high at the top of a flag staff, the depression angle of 30° is made. Also, looking at the bottom of the staff from the tower, the angle of the depression made is of 60°. Find the height of the flag staff.
उत्तर
In the figure, PQ is the tower of height 10 m and AB is the flagstaff.
∠MPB = ∠PBQ, ∠MPA = ∠PAS ......(Alternate interior angles)
Now, in ΔPBQ
tan 60° = `(PQ)/(BQ)`
⇒ `sqrt(3) = 10/(BQ)`
⇒ BQ = `10/sqrt(3)`
Also, in ΔPAS
tan 30° = `(PS)/(AS)`
⇒ `1/sqrt(3) = (PS)/(BQ)` ......[∵ BQ = AS]
⇒ `1/sqrt(3) = (PS)/(10/sqrt(3)) = (sqrt(3) PS)/10`
⇒ `sqrt(3) xx sqrt(3) PS` = 10
⇒ 3 PS = 10
⇒ PS = `10/3`
So, SQ = AB = PQ – PS
= `10 - 10/3`
= `(3 xx 10 - 10)/3`
= `20/3`
= 6.67
As a result, the flagstaff's height is 6.67 m.
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