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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
times as long as its shadow or height ??



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So let the height of the flag staff be h 

and the height of the shadow be x when the sun rays makes a angle 60° with the ground

so let the angle at the instant be Ф 

so tan 60 = h/x ............. i

and tan Ф = h/3x ....... ii

so using i

⇒ h/x = √3

⇒ h/3x = √3/3    (multiplying 3 on divisor of both sides)

⇒ tan Ф = 1/√3                 {since,  tan Ф = h/3x}

⇒ Ф = 30°

so the angle at the instant is 30° ANSWER
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