Observing from the top of a tower,the angles | vedclass

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

Question

(B) Let $H$ be the height of the tower and $h = 100 \, m$ be the height of the building.Let $x$ be the distance between the tower and the building.Fro

Vedclass · Accepted Answer

$150$

Vedclass · Answer

(B) Let $H$ be the height of the tower and $h = 100 \, m$ be the height of the building.Let $x$ be the distance between the tower and the building.From the top of the tower,the angle of depression to the top of the building is $30^{\circ}$,so the angle of elevation from the top of the building to the top of the tower is $30^{\circ}$.Thus,$	an(30^{\circ}) = \frac{H - 100}{x} \implies \frac{1}{\sqrt{3}} = \frac{H - 100}{x} \implies x = \sqrt{3}(H - 100)$.From the top of the tower,the angle of depression to the bottom of the building is $60^{\circ}$,so the angle of elevation from the bottom of the building to the top of the tower is $60^{\circ}$.Thus,$	an(60^{\circ}) = \frac{H}{x} \implies \sqrt{3} = \frac{H}{x} \implies x = \frac{H}{\sqrt{3}}$.Equating the two expressions for $x$: $\sqrt{3}(H - 100) = \frac{H}{\sqrt{3}}$.$3(H - 100) = H \implies 3H - 300 = H \implies 2H = 300 \implies H = 150 \, m$.

Observing from the top of a tower,the angles of depression of the top and the bottom of a $100 \, m$ high building are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower in $m$.

Similar Questions

From the top of a hill $100\, m$ high,the angles of depression of the top and the bottom of a tower are observed to be $30^{\circ}$ and $45^{\circ}$ respectively. Find the height of the tower in $m$.

$A$ person is watching from a point $A$ on the ground,which is $x \ m$ away from the base of a building. The height of the building is $y \ m$ and the angle of elevation of the top of the building is found to be $70^\circ$. Then:

From a balloon vertically above a straight road,the angles of depression of two cars at an instant are found to be $45^{\circ}$ and $60^{\circ}$. If the cars are $100 \, m$ apart,find the height of the balloon.

$A$ ladder $15 \, m$ long just reaches the top of a vertical wall. If the ladder makes an angle of $60^{\circ}$ with the wall,find the height of the wall in $m$.

The shadow of a tower standing on a level plane is found to be $50 \, m$ longer when the Sun's elevation is $30^{\circ}$ than when it is $60^{\circ}$. Find the height of the tower (in $m$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module