A spherical balloon of radius 60 cm subtends an angle of 60 degrees at a man's eye when the angle - Maths - Some Applications of Trigonometry

Question

A spherical balloon of radius 60 cm subtends an angle of 60 degrees
at a man's eye when the angle of elevation of it's centre is 45
degree Find the height of the centre of the balloon

Ashwini Kumar · Accepted Answer

Let BC be the height of centre of baloon, and height of top of baloon is BD
Here, CD= 60 cm∠BAD=60° and ∠BAC=45°In right angled triangle BAC,tan45°=BCAB⇒1=BCAB∴AB=BCNow in triangle BAD,tan60°=BC+60AB⇒3=BC+60BC⇒3 BC=BC+60⇒3 -1BC=60⇒BC=603-1=603+13-13+1=603+13-1=603+12=303+1=301
732+1=30×2 732=81 96 cm

A spherical balloon of radius 60 cm subtends an angle of 60 degrees at a man's eye when the angle of elevation of it's centre is 45 degree. Find the height of the centre of the balloon.