a person standing at the foot of a tower walks 3a meters away from it and observes the angle of - Maths - Some Applications of Trigonometry

Question

a person standing at the foot of a tower walks 3a meters away from
it and observes the angle of elevation to be alpha He then walks a
distance 4a perpendicular to the previous direction and observes
the angle to be beta,then find the height of the tower in terms of
beta?

Anuradha Sharma · Accepted Answer

Here AB is the tower and initially person is at A now he wals 3a to reach C and from there he will reach at D to cover a distance 4a and here visualizationis required as he will travell in horizontal direction so angle DAB will be 90 degreeNow in right angle triangle ACD, AD=CD2+AC2=9a2+16a2=5aNow angle ACB is α and angle ADB is β
So in right angle triangle ADB, tanβ=ABAD=AB5aAB = 5a tanβSo height of tower = AB=  5a tanβ unit

a person standing at the foot of a tower walks 3a meters away from it and observes the angle of elevation to be alpha.He then walks a distance 4a perpendicular to the previous direction and observes the angle to be beta,then find the height of the tower in terms of beta?