16)the angle of elevation of the top of a tower from a point A on the ground is 30 degree - Maths - Some Applications of Trigonometry

Question

16)the angle of elevation of the top of a tower from a
point A on the ground is 30 degree on moving a distance of 20metres
towards the foot of the tower to a point B the angle of elevation
increases to 60 degree find the height o the tower and the distance
of the tower from the point A

ramandeep.singh · Accepted Answer

Let the height of the tower be h m In right Î”DCB, $\tan 60^{0} = \frac{D C}{C B} \Rightarrow \sqrt{3} = \frac{h}{x} ∴ x = \frac{h}{\sqrt{3}}$ In right Î”DCA, $\tan 30^{0} = \frac{D C}{C A} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{x + 20} \Rightarrow \frac{h}{\sqrt{3}} + 20 = \sqrt{3} h ∴ h = 10 \sqrt{3} m ∴ x = \frac{10 \sqrt{3}}{\sqrt{3}} = 10 m$ Thus, distance of tower from point A = x + 20 = 30 m

16)the angle of elevation of the top of a tower from a point A on the ground is 30 degree.on moving a distance of 20metres towards the foot of the tower to a point B the angle of elevation increases to 60 degree.find the height o the tower and the distance of the tower from the point A.