Observing from the top of a 150, m high tower | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the height of the tower be $AB = 150\, m$ and the position of the cycle be $C$.The angle of depression from the top $A$ to the cycle $C$ is $6

Vedclass · Accepted Answer

$50\sqrt{3}\, m$

Vedclass · Answer

(A) Let the height of the tower be $AB = 150\, m$ and the position of the cycle be $C$.The angle of depression from the top $A$ to the cycle $C$ is $60^{\circ}$,which implies the angle of elevation from $C$ to $A$ is also $60^{\circ}$ (alternate interior angles).In the right-angled triangle $ABC$,we have $	an(60^{\circ}) = \frac{	ext{Opposite}}{	ext{Adjacent}} = \frac{AB}{BC}$.Substituting the values: $\sqrt{3} = \frac{150}{BC}$.Therefore,$BC = \frac{150}{\sqrt{3}} = \frac{150\sqrt{3}}{3} = 50\sqrt{3}\, m$.Using $\sqrt{3} \approx 1.732$,we get $BC \approx 50 	imes 1.732 = 86.6\, m$.

Observing from the top of a $150\, m$ high tower,the angle of depression of a cycle on the ground is found to be $60^{\circ}$. How far away is the cycle from the tower?

Similar Questions

$A$ ladder leans against a wall. It makes an angle of $45^{\circ}$ with the ground and reaches a height of $10 \, m$ on the wall. Find the length of the ladder and the distance between the lower end of the ladder and the base of the wall.

As observed from the top of a $510 \ m$ high tower,the angles of depression of two houses situated in the east and west of the tower are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the distance between the two houses (in $m$).

The approximate value of $\frac{1}{\sqrt{3}}$ up to $2$ decimal places is.........

The angle of depression of the base of a tower from the top of a cliff is $60^{\circ}$ and the angle of elevation of the top of the tower from the base of the cliff is $30^{\circ}$. If the height of the tower is $50 \, m$,find the height of the cliff in meters.

The angles of depression of two cars parked in the same direction of a $50\, m$ high tower are found to be $30^{\circ}$ and $60^{\circ}$. Find the distance between these two cars. (in $, m$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module