Question

If the ratio between the length of the shadow of a tower and it's height is root3:1, then what is the angle of elevation of sun ?

Answer 1

See attachment, here AB is the height of tower and BC is the length of Shadow .
θ is the elevation angle of sun .
According to question ,
length of Shadow : height of tower = √3 : 1
⇒BC : AB = √3 : 1
⇒ BC/AB = √3/1
⇒ AB/BC = 1/√3

But AB/BC = tanθ [∵ tanФ = perpendicular/base ]
now, tanθ = 1/√3 = tan30°
∴ θ = 30° , hence elevation angle of sun is 30°

Answer 2

Length of shadow:Height of tower
=√3:1
BC:AB=√3:1
BC/AB=√3/1
AB/BC=1/√3


But AB/BC =tan theta
tan theta =1/√3=tan 30°

Hence,angle of elevation of the sun is 30°