From the top of a hill 100 , m high,the angle | vedclass

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

Question

(C) Let $AC$ be the hill of height $100 \, m$ and $ED$ be the tower.Let $EB$ be the horizontal line from $E$ to the hill $AC$,where $B$ is on $AC$.Giv

Vedclass · Accepted Answer

$42$

Vedclass · Answer

(C) Let $AC$ be the hill of height $100 \, m$ and $ED$ be the tower.Let $EB$ be the horizontal line from $E$ to the hill $AC$,where $B$ is on $AC$.Given: $AC = 100 \, m$,$\angle XAE = 30^{\circ}$,and $\angle XAD = 45^{\circ}$.Since $AX \parallel ED$,we have $\angle AEB = 30^{\circ}$ and $\angle ADC = 45^{\circ}$ (alternate interior angles).In right-angled $\Delta ACD$,$	an(45^{\circ}) = \frac{AC}{DC}$.$1 = \frac{100}{DC} \implies DC = 100 \, m$.Since $EDCB$ is a rectangle,$EB = DC = 100 \, m$ and $BC = ED$.In right-angled $\Delta ABE$,$	an(30^{\circ}) = \frac{AB}{EB}$.$\frac{1}{\sqrt{3}} = \frac{AB}{100} \implies AB = \frac{100}{\sqrt{3}} \approx 57.74 \, m$.Height of the tower $ED = BC = AC - AB = 100 - 57.74 = 42.26 \, m$.Rounding to the nearest integer,the height is $42 \, m$.

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 meters.

Similar Questions

$A$ $1.5 \, m$ tall boy is standing at some distance from a $30 \, m$ tall building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ}$ to $60^{\circ}$ as he walks towards the building. Find the distance he walked towards the building.

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 $m$.

From the top of a $70\, m$ tall tower,the angle of depression of the top and the base of a pole are found to be $30^{\circ}$ and $45^{\circ}$ respectively. Find the distance of the pole from the tower and the height of the pole.

Write 'True' or 'False' and justify your answer.
If the height of a tower and the distance of the point of observation from its foot,both,are increased by $10 \%$,then the angle of elevation of its top remains unchanged.

From a point $A$,$h \text{ m}$ above the ground level,the angle of elevation of the top of a tower is $\alpha$ and the angle of depression of the base of the tower is $\beta$. Prove that the height of the tower is $\frac{h(\tan \alpha + \tan \beta)}{\tan \beta} \text{ m}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module