Question

when the top of the tower is observed 30m away from its base the angle of elevation is 30 degree calculate the height of Tower

Answer 1

Answer- The above question is from the chapter 'Some Applications of Trigonometry'.

Given question: When the top of the tower is observed 30 m away from its base the angle of elevation is 30°, calculate the height of tower.

Solution: Let AB = Height of tower = ?

BC = Distance between tower and point of observation = 30 m

θ = 30°

(Diagram has been attached.)

$\dfrac{AB}{BC} = tan \: 30^{\circ}$

$\dfrac{AB}{30} = \dfrac{1}{\sqrt{3}}$

$\implies AB = \dfrac{30}{\sqrt{3}}$

$\implies AB = 10 \sqrt{3} \: m$

∴ Height of tower = 10√3 m