A tower subtends an angle of 30 degree at a point on the same level as its foot At - Maths - Introduction to Trigonometry

Question

A tower subtends an angle of 30 degree at a point on the same
level as its foot At a second point h metres above the first the
angle of depression of the foot of the tower is 60 degree The
height of the tower is ?

Ajanta Trivedi · Accepted Answer

let the height of the tower be AB let D be the first point where the tower subtends angle 30 deg C be the other point such that CD=h m from C the angle of depression of the foot of the tower be 60 deg in the right angled triangle CDB $\tan 60 = \frac{C D}{B D} B D = C D \cot 60 = \frac{h}{\sqrt{3}} m$ in the right angled triangle ABD, $\tan 30 = \frac{A B}{B D} A B = B D \tan 30 = \frac{h}{\sqrt{3}} \times \frac{1}{\sqrt{3}} = \frac{h}{3} m$ the height of the tower is h/3 m

A tower subtends an angle of 30 degree at a point on the same level as its foot. At a second point h metres above the first the angle of depression of the foot of the tower is 60 degree. The height of the tower is ?