9) a vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres - Maths - Some Applications of Trigonometry

Question

9) a vertical tower stands on a horizontal plane and is
surmounted by a vertical flag-staff of height 5 metres at a point
on the plane,the angles of elevation of the bottom and the top of
the flag-staff are respectively 30 degree and 60 degree find the
height of the tower

ramandeep.singh · Accepted Answer

Let h be the height of the tower In right Î”DBC, $\tan 30^{0} = \frac{D B}{B C} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{x} ∴ x = \sqrt{3} h$ In right Î”ABC, $\tan 60^{0} = \frac{A B}{B C} \Rightarrow \sqrt{3} = \frac{h + 5}{x} \Rightarrow 3 h = h + 5 ∴ h = 2 5 m$ Thus, height of the tower = 2 5 m

9) a vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres.at a point on the plane,the angles of elevation of the bottom and the top of the flag-staff are respectively 30 degree and 60 degree.find the height of the tower.