From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression to the foot of the tower. The height of the tower is ___.

25m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

75m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

50m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

100m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
50m

In triangle ABE,

$t a n θ_{2}$ = $\frac{A B}{B E}$ = $\frac{25}{B E}$

In triangle ADC,

$t a n θ_{1}$ = $\frac{C D}{A D}$

We know, $θ_{1}$ = $θ_{2}$

$\Rightarrow$ $t a n θ_{1}$ = $t a n θ_{2}$

$\frac{C D}{A D}$ = $\frac{25}{B E}$

$\Rightarrow$ CD = 25 [Since AD = BE]

DE =AB = 25m

$\Rightarrow$ Height of tower = CD+ DE
= 25+25 = 50m

Suggest Corrections

Similar questions

From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression to the foot of the tower. The height of the tower is ___.

Two towers A and B are standing at some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be $30^{\circ}$ . From the top of tower B, the angle of depression of the foot of tower A is found to be $60^{\circ}$ . If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is _____ m

Join BYJU'S Learning Program

From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression to the foot of the tower. The height of the tower is ___.

The correct option is C 50m In triangle ABE, tanθ2 = ABBE = 25BE In triangle ADC, tanθ1 = CDAD We know, θ1 = θ2 ⇒ tanθ1 = tanθ2 CDAD = 25BE ⇒ CD = 25 [Since AD = BE] DE =AB = 25m ⇒ Height of tower = CD+ DE = 25+25 = 50m