Q. 6] From a point in the cricket ground ,the angle of elevation of a vertical tower is found to be theta (Ꝋ) at a distance of 200 from the tower. On walking 125 metre towards the tower the angle of elevation becomes 2 Ꝋ, find the height of tower ? प्र.6] क्रिकेटच्या मैदानावरील एका बिंदूपासून पाहिले असता एका उभ्या टॉवरचा टॉवर पासून 200 मी अंतेरवरील बिन्दुशी होणारा उन्नत कोन Ꝋआहे . टॉवरच्या दिशेने 125 मी चालले असता उन्नत कोन 2 Ꝋ होतो ,तर टॉवरची उंची काढा . *
a)300m
b)100m
c)400m
d)200m
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Thus the height of tower=100 m
Step-by-step explanation:
In the Δ PQA
tan θ =PQ/QA
or tan θ= h/200
h=200*tanθ.................(1)
In the Δ PQB
tan 2θ =PQ/QB=h/(200-125)
2tanθ/(1- tan²θ) =h/75
From(1) putting value of h
2tanθ/(1- tan²θ) =200*tanθ/75
1 /(1-tan²θ) =100/75=4/3
4*( 1-tan²θ)=3
1-tan²θ =3/4
tan²θ =1-3/4=1/4
tan θ =1/2
Thus from (1)
h=200*1/2=100
Thus the height of tower=100 m
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