Question

a tower subtends an angle alpha at a point A in the plane of its base and the angel of depression of the foot of the tower at a point b meter just above A is beta. Prove ther the height of the tower is b tan alpha cot beta.

Answer 1

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Answer 2

Answer:

The height of the tower is b.tanα cotβ  is proved as follows:

Step-by-step explanation:

Step 1:

Given Data: Assume x be the distance of the point A and h be height of the tower.

Step 2:

In △APQ,  (In an Angle APQ)

h = x tanα ……………………..(i)

Step 3:

In △PRB,  (In an angle PRB)

b = x tanβ ……………………....(ii)

Step 4:

From Equation (i) and Equation (ii)

h = b.tanα/ tanβ = b.tanα cotβ