Question

from the top of a building h m high, the angle of elivation from the top of the pole is found to be a, while the angle of depression of the base of the pole is found to be b, prove that the height of the pole is h(1+tan a + cot b)m​

Answer 1

height of the pole = h (1  -  TanaCotb)

Step-by-step explanation:

b = Horizontal distance between pole & buiding

x = height of pole

Tan a  = ( h - x)/ b

=> b = (h - x) / Tana

Tan b = h/b

=> b = h/Tanb

Equating both

(h - x) / Tana  = h/Tanb

=> hTanb - xTanb   = hTana

=> xTanb = hTanb - h Tana

=> x = h - hTana/Tanb

=> x = h - hTanaCotb

=> x = h (1  -  TanaCotb)

height of the pole = h (1  -  TanaCotb)

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