(D) Let the height of the object be $h$. Let $B$ be the point on the ground directly below the object $A$, and $C$ and $D$ be the two points on the gr

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

$\frac{d}{\cot \alpha-\cot \beta}$

(D) Let the height of the object be $h$. Let $B$ be the point on the ground directly below the object $A$, and $C$ and $D$ be the two points on the ground such that $CD = d$ and $BD = x$.In $\triangle ABC$, $\tan \alpha = \frac{h}{x+d} \Rightarrow x+d = h \cot \alpha$ $(i)$In $\triangle ABD$, $\tan \beta = \frac{h}{x} \Rightarrow x = h \cot \beta$ (ii)Substituting the value of $x$ from (ii) into $(i)$:$h \cot \beta + d = h \cot \alpha$$d = h \cot \alpha - h \cot \beta$$d = h(\cot \alpha - \cot \beta)$$h = \frac{d}{\cot \alpha - \cot \beta}$

Class 11 Mathematics Trigonometrical Equations Height and Distance

Difficult

The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object, the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

TS EAMCET 2007 All TS EAMCET

AP EAMCET 2007 All AP EAMCET

A
$d \tan \alpha$
B
$d \cot \beta$
C
$\frac{d}{\cot \alpha+\cot \beta}$
D
$\frac{d}{\cot \alpha-\cot \beta}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Equations

Subtopic

Height and Distance

Previous Year

TS EAMCET 2007 Paper All TS EAMCET years →

Previous Year

AP EAMCET 2007 Paper All AP EAMCET years →

From the top of a hill $h$ metres high, the angles of depression of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in metres) of the pillar is

MediumTS EAMCET 2008

View Solution

$A$ flag-post $20 \ m$ high standing on the top of a house subtends an angle whose tangent is $\frac{1}{6}$ at a distance $70 \ m$ from the foot of the house. The height of the house is......$m$

Difficult

View Solution

The sum of the angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it is $90^{\circ}$. Then,the height of the tower is

DifficultTS EAMCET 2010

View Solution

$A$ man from the top of a $100 \ m$ high tower sees a car moving towards the tower at an angle of depression of $30^\circ$. After some time,the angle of depression becomes $60^\circ$. The distance (in meters) travelled by the car during the time is

MediumIIT 2001

View Solution

The angle of elevation of the top of a pillar at a point $A$ on the ground is $15^\circ$. On walking $40 \ m$ towards the pillar,the angle becomes $30^\circ$. The height of the pillar is $... \ m$.

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

The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object, the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

Similar Questions

From the top of a hill $h$ metres high, the angles of depression of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in metres) of the pillar is

$A$ flag-post $20 \ m$ high standing on the top of a house subtends an angle whose tangent is $\frac{1}{6}$ at a distance $70 \ m$ from the foot of the house. The height of the house is......$m$

The sum of the angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it is $90^{\circ}$. Then,the height of the tower is

$A$ man from the top of a $100 \ m$ high tower sees a car moving towards the tower at an angle of depression of $30^\circ$. After some time,the angle of depression becomes $60^\circ$. The distance (in meters) travelled by the car during the time is

The angle of elevation of the top of a pillar at a point $A$ on the ground is $15^\circ$. On walking $40 \ m$ towards the pillar,the angle becomes $30^\circ$. The height of the pillar is $... \ m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module