the shadow of a flagstaff is 3 times as long as the shadow of the flagstaff when the sun rays - Maths - Some Applications of Trigonometry

Question

the shadow of a flagstaff is 3 times as long as the shadow of
the flagstaff when the sun rays meet the ground at an angle of 60
deg find the angle between the sun rays and the ground at the time
of longer shadow

Lalit Mehra · Accepted Answer

Dear Student!

Let the height of the flagstaff be h m and the angle between the sun rays and the ground at the time of longer shadow be Î¸ BC and BD are the lengths of the shadow of the flagstaff when the angle between the sunrays and the ground are 60Â° and Î¸ respectively Given, BD = 3 BC (1) In Î”ABC, $\tan 60 ° = \frac{AB}{BC} ∴ \sqrt{3} = \frac{h}{BC} \Rightarrow h = \sqrt{3} BC (2)$ In Î”ABC, $\tan θ = \frac{AB}{BD} ∴ \tan θ = \frac{h}{BD} \Rightarrow h = \tan θ \times BD (3)$ From (1), (2) and (3), we get $\sqrt{3} BC = \tan θ \times 3 BC ∴ \tan θ = \frac{\sqrt{3}}{3} = \frac{1}{\sqrt{3}} \Rightarrow θ = 30 ° (∵ \tan 30 ° = \frac{1}{\sqrt{3}})$ Thus, the angle between the sunrays and the ground at the time of longer shadow is 30Â° Cheers!

the shadow of a flagstaff is 3 times as long as the shadow of the flagstaff when the sun rays meet the ground at an angle of 60 deg. find the angle between the sun rays and the ground at the time of longer shadow.