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Question
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
Options
\[\frac{h}{2} m\]
\[\sqrt{3h} m\]
\[\frac{h}{3} m\]
\[\frac{h}{\sqrt{3}}m\]
Solution
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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Read the following passage:
A boy is standing on the top of light house. He observed that boat P and boat Q are approaching the light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. He also knows that height of the light house is 100 m.
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Based on the above information, answer the following questions.
- What is the measure of ∠APD?
- If ∠YAQ = 30°, then ∠AQD is also 30°, Why?
- Find length of PD
OR
Find length of DQ
