The angle of elevation of the top of a tower from a point on the same level as the foot - Maths - Some Applications of Trigonometry

Question

The angle of elevation of the top of a tower from a point on the
same level as the foot of the tower is 30 degree On advancing 150m
towards the foot of the tower, the angle of elevation becomes 60
degree Find the height of the tower

Ayush Jha · Accepted Answer

We can plot the following diagram from the given data as-

Use trigonometric ratios in the triangle ABD, $\tan 60^{o} = \frac{h}{a} h = \sqrt{3} a$ (1) Similarly using trigonometric ratios in the triangle ABC, we get, $\tan 30^{o} = \frac{h}{a + 150} \sqrt{3} h = 150 + a$ (2) Use equation(1) in equation (2), $a = 75$ (3) Put the value of a in equation(1) to get the value of h, $h = 75 \sqrt{3} = 75 (1 732) = 129 9 m$ Therefore the height of the tower is 129 9 m

The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is 30 degree. On advancing 150m towards the foot of the tower, the angle of elevation becomes 60 degree. Find the height of the tower.