(D) Let the height of the tower $NM = H$ and the distance $LM = x$.In $\triangle NQM$,$\tan 60^{\circ} = \frac{NM}{QM} \implies \sqrt{3} = \frac{H}{QM

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

(D) Let the height of the tower $NM = H$ and the distance $LM = x$.In $\triangle NQM$,$\tan 60^{\circ} = \frac{NM}{QM} \implies \sqrt{3} = \frac{H}{QM} \implies QM = \frac{H}{\sqrt{3}}$.In $\triangle NLM$,$\tan 30^{\circ} = \frac{NM}{LM} \implies \frac{1}{\sqrt{3}} = \frac{H}{x} \implies x = H\sqrt{3}$.Since the height $H$ of the tower is not provided,the exact numerical value of $x$ cannot be determined.Therefore,the data is inadequate.

Competitive Quantitative Aptitude Heights and Distances Heights and Distances

Easy

$A$ man standing at a point $P$ (or $L$ in the diagram) is watching the top of a tower $N$,which makes an angle of elevation of $30^{\circ}$ with the man's eye. The man walks some distance towards the tower to point $Q$ to watch its top and the angle of elevation becomes $60^{\circ}$. What is the distance (in units) between the base of the tower $M$ and the point $P$ (or $L$)?

A
$4 \sqrt{3}$
B
$8$
C
$12$
D
Data inadequate

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Heights and Distances

Subtopic

Heights and Distances

If $r \sin \theta = 1$ and $r \cos \theta = \sqrt{3}$,then the value of $(\sqrt{3} \tan \theta + 1)$ is

Easy

View Solution

$A$ man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^{\circ}$. When he moves $36 \ m$ away from the bank,he finds the angle to be $30^{\circ}$. Find the breadth of the river (in $m$).

Medium

View Solution

From the top of a $60 \ m$ high lighthouse with its base at sea level,the angle of depression of a boat is $15^{\circ}$. The distance of the boat from the lighthouse is

Medium

View Solution

$A$ $20 \, m$ high electric pole stands upright on the ground with the help of a steel wire attached to its top and fixed on the ground. If the steel wire makes an angle of $60^{\circ}$ with the horizontal ground,find the length of the steel wire (in $m$).

Easy

View Solution

$A$ person of height $6 \ ft$ wants to pluck a fruit which is on a $\frac{26}{3} \ ft$ high tree. If the person is standing $\frac{8}{\sqrt{3}} \ ft$ away from the base of the tree,then at what angle should he throw a stone so that it hits the fruit (in $^{\circ}$)?

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

If $r \sin \theta = 1$ and $r \cos \theta = \sqrt{3}$,then the value of $(\sqrt{3} \tan \theta + 1)$ is

$A$ man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^{\circ}$. When he moves $36 \ m$ away from the bank,he finds the angle to be $30^{\circ}$. Find the breadth of the river (in $m$).

From the top of a $60 \ m$ high lighthouse with its base at sea level,the angle of depression of a boat is $15^{\circ}$. The distance of the boat from the lighthouse is

$A$ $20 \, m$ high electric pole stands upright on the ground with the help of a steel wire attached to its top and fixed on the ground. If the steel wire makes an angle of $60^{\circ}$ with the horizontal ground,find the length of the steel wire (in $m$).

$A$ person of height $6 \ ft$ wants to pluck a fruit which is on a $\frac{26}{3} \ ft$ high tree. If the person is standing $\frac{8}{\sqrt{3}} \ ft$ away from the base of the tree,then at what angle should he throw a stone so that it hits the fruit (in $^{\circ}$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module