Question

At an instant the shadow of a flag-staff is three times as long as its shadow, when the sun-rays make an angle of 60 with the ground. Find the angle between the sun-rays and the ground at this instant. 16

Answer 1

See diagram for details.
Let AB be flagpole.
BC be shadow at 60°
BD be shadow at θ°

To find: Angle θ°

BD = 3BC (as per question) ...(1)

Therefore,
=> tan 60° = AB/BC
=> √3 = AB/BC
=> AB = BC√3 ...(2)

=> tan θ° = AB/BD
= BC√3/3BC (From 1 and 2)
= √3/3
= 1/√3

∴ tan θ° = 1/√3
∴ tan θ° = tan 30°
∴ θ° = 30°

Therefore the angle at the instant is 30°.

Answer 2

$\textbf{Answer is in Attachment !}$