Q) The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is 60°. The angle of elevation of the top of second tower from the foot of the first tower is 30°. Find the distance between two towers and the height of the other tower. Also, find the length of the wire attached to the tops of both the towers.


The angle of elevation_Trigonometry Application

Let AB and CD be the towers where AB is first tower of 24m height

Let Height of the other tower be h and distance between both of the towers be d

Therefore, in Δ BAC, tan 60°  =  \frac{24}{d}

\therefore       √3 = \frac{24}{d}   or d =  8√3 m

Also, in Δ DAC, tan 30° =  \frac{h}{d}

\therefore        h = \frac{d}{\sqrt3}  or h = 8 m

Calculation for Length of the wire BD in Δ BDE:

BD2 = (24 – 8)2 + (8 √3)2 = 162  + (8 √3)

BD2 =  256 + 192 = 448

BD = √448  = 8√7 m

Therefore, the length of wire between tops of two towers is 8√7 m

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