Question

A boy observes that the angle of elevation of the top of the tower is 32°. He then walks 8m towards the tolerated then discover the angle of elevation is 43°. Find the height of the tower.

Answer 1

Let the height of the tower be h and the distance of the boy from the foot of the tower be d. then tan 32=h/d,

h=d.tan32, take 32 as 30,

h=d.tan30=d/√3 equation 1

When he has walked 8 m towards the tower,

tan 43=h/(d-8)

h=(d-8).tan 43 take 43as 45

h=(d-8).tan45=(d-8)×1=d-8

d/√3=d-8

d-d/√3=8

d(1-1/√3)=8

d(√3-1)=8√3

d=8√3/(√3-1)=8√3(√3+1)/{(√3-1)(√3+1)}=8√3(√3+1)/(3-1)=4√3(√3+1)

h=d/√3=4(√3+1)

Take the value of h from equation 1