Question

the angle of elevation of a tower from a point on the same level at the foot of the tower is 30°.on advancing 150m towards the foot of the tower the foot of the tower the angle of elevation of the tower becomes 60.find the height of the tower

Answer 1

this is the answer for your question

Answer 2

Answer: The height of the tower is 129.9 m.

Step-by-step explanation:

Since we have given that

In ΔABC,

we will use "Trigonometric Ratios":

$\tan \theta=\frac{AB}{BC}\\\\\tan 60=\frac{x}{BC}\\\\\sqrt{3}=\frac{x}{BC}\\\\BC=\frac{x}{\sqrt{3}}$

Similarly, In ΔABD,

$\tan \theta=\frac{AB}{BD}\\\\\tan 30=\frac{x}{BC+150}\\\\\frac{1}{\sqrt{3}}=\frac{x}{BC+150}\\\\BC+150=x\sqrt{3}\\\\\frac{x}{\sqrt{3}}+150=x\sqrt{3}\\\\150=x\sqrt{3}-\frac{x}{\sqrt{3}}\\\\150\sqrt{3}=3x-x\\\\150\sqrt{3}=2x\\\\x=75\sqrt{3}=129.9\ m$

Hence, the height of the tower is 129.9 m.