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Shayan Aatif
Subject: Maths
, asked on 3/2/18
Plz tell fast
Q.
A ladder rests against a wall at an inclination of
$\alpha $
to the horizontal. It's foot is pulled away from the wall through a distance 'p' so that its upper end slides a distance 'q' down the wall and then the ladder makes an angle
$\beta $
to the horizontal. Show that :-
$\frac{p}{q}=\frac{\mathrm{cos}{\displaystyle}{\displaystyle \beta}{\displaystyle}{\displaystyle -}{\displaystyle}{\displaystyle \mathrm{cos}}{\displaystyle \alpha}}{\mathrm{sin}{\displaystyle}{\displaystyle \alpha}{\displaystyle}{\displaystyle -}{\displaystyle}{\displaystyle \mathrm{sin}}{\displaystyle}{\displaystyle \beta}}$
Answer
1
Shishira
Subject: Maths
, asked on 31/1/18
The angle of depression of the rop and bottom of building is 50m. As observed from top are 30 and 60. Find the height of the tower and horizontal distance between the building and tower
Answer
1
Gouri Lahoti
Subject: Maths
, asked on 31/1/18
Question no.7
$7.\left(\mathrm{tan}\theta +2\right)\left(2\mathrm{tan}\theta +1\right)=5\mathrm{tan}\theta +se{c}^{2}\theta .$
Answer
2
Gouri Lahoti
Subject: Maths
, asked on 29/1/18
Q.3. The shadow of a tower standing on a plane level is found to be 50 m. longer when Sun's elevation is 30
$\xb0$
than when it is 60
$\xb0$
. Find the height of the tower.
Answer
1
Prakhar Nigam
Subject: Maths
, asked on 26/1/18
An aeroplane was flying at a height of 7000 root 3 m above the ground. From
two observation points, the angles of elevation of the aeroplane were
recorded as 30 degree and 60 degree at the same time. Assume that at that particular
instance, the aeroplane was directly above the line joining the two
observation points.
Answer
1
Angela
Subject: Maths
, asked on 25/1/18
A boy standing on a horizontal plane finds a kite flying at a distance of 150 m from him at an angle of of elevation of 30 degree. A girl standing on the roof of 30 m high building finds the angle of elevation of the same kite to be 45 degree. Find the distance of the kite from the girl?
Answer
1
Roshni Majumder
Subject: Maths
, asked on 20/1/18
A ladder rests against a vertical wall at an inclination of 60 degrees to the horizontal. Its foot is pulled away from the wall through a distance "p"m so that the upper end slides down a distance of "q" m along the wall and then the ladder makes an angle 45 degrees to the horizontal. Find the value of p/q.
Answer
2
Suyash Jain
Subject: Maths
, asked on 14/1/18
Q. A round of balloon radius 'r' subtends an angle at the eye of the observer while the angle
$\alpha $
of elevation of its centre is ß. Prove that the height Of the centre of the balloon is r sin ß cosec
$\alpha $
/2.
Answer
1
Yasmine
Subject: Maths
, asked on 14/1/18
10th one pls
Answer
1
Yasmine
Subject: Maths
, asked on 14/1/18
Q. 6. The angle of elevation of the top of a tower from a point on the ground, which is
30 m away from the foot Of the tower is 30 degree. Find the height of the tower.
Answer
2
Kritika Chhikara
Subject: Maths
, asked on 13/1/18
An aircraft is flying along a horizontal path PQ directly towards an observer on the ground at O and maintaining an altitude of 3000m. When the aircraft is at P, the angle of depression is 30 and when at Q, the angle of depression is 60. Find the distance of PQ.
Answer
2
Yasmine
Subject: Maths
, asked on 13/1/18
How did root 3x/ 3x become 1/root3
$\mathrm{tan}\theta =\frac{\sqrt{3}x}{3x}=\frac{1}{\sqrt{3}}\Rightarrow \theta =30\xb0$
Answer
3
Yasmine
Subject: Maths
, asked on 13/1/18
$\mathit{H}\mathit{o}\mathit{w}\mathbf{}\mathit{d}\mathit{i}\mathit{d}\mathbf{}\mathbf{4}\mathbf{}\mathit{c}\mathit{o}\mathit{t}\mathbf{}\mathit{\theta}\mathbf{}\mathbf{\times}\mathbf{}\mathbf{9}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{\theta}\mathbf{}\mathit{b}\mathit{e}\mathit{c}\mathit{o}\mathit{m}\mathit{e}\mathbf{}\mathbf{36}\frac{\mathbf{1}}{\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{}\mathbf{\theta}}\mathbf{}\mathbf{\times}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{\theta}\mathbf{}\mathbf{:}$
$\Rightarrow \frac{h}{4}=cot\theta \phantom{\rule{0ex}{0ex}}\Rightarrow h=4cot\theta \phantom{\rule{0ex}{0ex}}In\u25b3ABQ,\frac{AB}{QB}=\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}\frac{h}{9}=\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}h=9\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}Fromequation\left(i\right)and\left(ii\right),weget\phantom{\rule{0ex}{0ex}}h\times h=4cot\theta \times 9\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}\Rightarrow {h}^{2}=36cot\theta \times \mathrm{tan}\theta =36\frac{1}{\mathrm{tan}{\displaystyle \theta}}\times \mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}\Rightarrow {h}^{2}=36\Rightarrow h=6m.$
Answer
1
Yasmine
Subject: Maths
, asked on 13/1/18
Q. A TV tower stands vertically on a bank of a canal. From a point on the other bank direct opposite the tower is 60
$\xb0$
. From another point 20 m away from this point on the joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30
$\xb0$
(see the given figure). Find the height of the tower and the width of the canal.
Answer
2
Komal Gupta
Subject: Maths
, asked on 12/1/18
Solve this:
1) The angle of elevation of a cloud from a point 60m above a lake is 30
^{o}
and the angle of depression of the reflection of the cloud in the lake is 60
^{o}
. Find the height of the cloud from the surface of the lake.
2) The angle of elevation of a jet fighter from a point A on the ground is 60
^{o}
, After a flight of 10 seconds, the angle of elevation changes to 30
^{o}
. If the jet is flying at a speed of 432 km/hr, find the constant height at which the jet is flying.
Answer
1
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$\frac{p}{q}=\frac{\mathrm{cos}{\displaystyle}{\displaystyle \beta}{\displaystyle}{\displaystyle -}{\displaystyle}{\displaystyle \mathrm{cos}}{\displaystyle \alpha}}{\mathrm{sin}{\displaystyle}{\displaystyle \alpha}{\displaystyle}{\displaystyle -}{\displaystyle}{\displaystyle \mathrm{sin}}{\displaystyle}{\displaystyle \beta}}$

$7.\left(\mathrm{tan}\theta +2\right)\left(2\mathrm{tan}\theta +1\right)=5\mathrm{tan}\theta +se{c}^{2}\theta .$

two observation points, the angles of elevation of the aeroplane were

recorded as 30 degree and 60 degree at the same time. Assume that at that particular

instance, the aeroplane was directly above the line joining the two

observation points.

A boy standing on a horizontal plane finds a kite flying at a distance of 150 m from him at an angle of of elevation of 30 degree. A girl standing on the roof of 30 m high building finds the angle of elevation of the same kite to be 45 degree. Find the distance of the kite from the girl?Q. 6. The angle of elevation of the top of a tower from a point on the ground, which is

30 m away from the foot Of the tower is 30 degree. Find the height of the tower.

$\mathrm{tan}\theta =\frac{\sqrt{3}x}{3x}=\frac{1}{\sqrt{3}}\Rightarrow \theta =30\xb0$

$\mathit{H}\mathit{o}\mathit{w}\mathbf{}\mathit{d}\mathit{i}\mathit{d}\mathbf{}\mathbf{4}\mathbf{}\mathit{c}\mathit{o}\mathit{t}\mathbf{}\mathit{\theta}\mathbf{}\mathbf{\times}\mathbf{}\mathbf{9}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{\theta}\mathbf{}\mathit{b}\mathit{e}\mathit{c}\mathit{o}\mathit{m}\mathit{e}\mathbf{}\mathbf{36}\frac{\mathbf{1}}{\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{}\mathbf{\theta}}\mathbf{}\mathbf{\times}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{\theta}\mathbf{}\mathbf{:}$$\Rightarrow \frac{h}{4}=cot\theta \phantom{\rule{0ex}{0ex}}\Rightarrow h=4cot\theta \phantom{\rule{0ex}{0ex}}In\u25b3ABQ,\frac{AB}{QB}=\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}\frac{h}{9}=\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}h=9\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}Fromequation\left(i\right)and\left(ii\right),weget\phantom{\rule{0ex}{0ex}}h\times h=4cot\theta \times 9\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}\Rightarrow {h}^{2}=36cot\theta \times \mathrm{tan}\theta =36\frac{1}{\mathrm{tan}{\displaystyle \theta}}\times \mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}\Rightarrow {h}^{2}=36\Rightarrow h=6m.$

Solve this:1) The angle of elevation of a cloud from a point 60m above a lake is 30

^{o}and the angle of depression of the reflection of the cloud in the lake is 60^{o}. Find the height of the cloud from the surface of the lake.2) The angle of elevation of a jet fighter from a point A on the ground is 60

^{o}, After a flight of 10 seconds, the angle of elevation changes to 30^{o}. If the jet is flying at a speed of 432 km/hr, find the constant height at which the jet is flying.