Question

A tower subtends an angle at a point A in the plane of its base and the angle of depression of

the foot of the tower at a point b metres just above A is . Prove that the height of tower is b

tan cot .​

Answer 1

Answer:

CD=btanαcotβ [ Hence proved ]

Step-by-step explanation:

Here, CD is the height of the tower.

In △ABC,tanβ=

AC

AB

⇒ tanβ=

AC

b

∴ AC=

tanβ

b

∴ AC=bcotβ ------ ( 1 )

In △ACD,tanα=

AC

CD

⇒ CD=tanα×AC

⇒ CD=tanα×bcotβ [ From ( 1 ) ]

∴ CD=btanαcotβ [ Hence proved ]

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