We have a question from trigonometry (height and distance) in which we have been asked to find the height of the flagstaff if the angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45∘. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60∘.

Book RS Aggarwal, Class 10, chapter 14, question no 5

Let AB is the tower of height h meter and AC is flagstaff of height x meter.

∠APB=45o and ∠BPC=60o

tan60o=(x+h)/120

√3=(x+h)/120

x=120√3−h

tan45o=h/120

1=h/120

h = 120

Substitute the value of h in x,

x=120√3−120

x=120(√3−1)

x=120(1.73−1)

x=87.6m

Therefore the height of the flagstaff = 87.6m