a man standing on the top of a multi-storey building, which is 30m high, observes the angle of elevation of - Maths - Some Applications of Trigonometry

Question

a man standing on the top of a multi-storey building, which is
30m high, observes the angle of elevation of the top of a tower as
60 degrees and the angle of depression of the base of the tower as
30 degrees Find the horizontal distance between the building and
the tower also find the height of the tower

Ajanta Trivedi · Accepted Answer

let the height of the building be CD = 30 m

let the height of the tower be AB = h m.

the angle of elevation of the top of the tower be ∠ACE= 60 deg

the angle of depression of the bottom of the tower be ∠ECD=30 deg

in the right angled triangle CEB ,

$\tan 30 = \frac{B E}{C E} \frac{1}{\sqrt{3}} = \frac{30}{C E} [∵ B E = D C = 30 m] C E = 30 \sqrt{3} m . C E = 30 * 1.73 = 51.9 m .$

in the triangle AEC,

$\tan 60 = \frac{A E}{C E} \sqrt{3} = \frac{A E}{30 \sqrt{3}} A E = \sqrt{3} * 30 \sqrt{3} = 30 * 3 A E = 90 m .$

therefore the horizontal distance between the building and the tower is 51.9 m.

and the height of the tower is AB=AE+EB=90+30=120 m.

hope this helps you.