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प्रश्न
A tower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is
विकल्प
\[\frac{h}{2} m\]
\[\sqrt{3h} m\]
\[\frac{h}{3} m\]
\[\frac{h}{\sqrt{3}}m\]
उत्तर
Let AB be the tower and C is a point on the same level as its foot such that ∠ACB = 30°
The given situation can be represented as,
Here D is a point h m above the point C.
In ΔBCD,
`⇒ tan B=(CD)/(CB)`
`⇒ tan 60°=h/(CB)`
`⇒ sqrt3=h/(CB)`
`⇒ CB=h/sqrt3`
Again in triangle ABC,
`tan C=(AB)/(CB)`
`⇒ tan30= (AB)/((h/sqrt3))` [Using (1)]
`⇒1/sqrt3=AB/((h/sqrt3))`
`⇒ AB=h/3`
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