The distances of three points on a pole from its foot are in $A . P$ . If the angles of elevation of these points from a point on the ground are $θ, ϕ, Ψ$ respectively, then
$cot ϕ$ $cot ψ, cot ψ cot θ cot ϕ$ are in $G . P$ .,

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B False
Ans. $F a l s e$
$O P = a cot θ = (a + d) cot ϕ$
$= (a + 2 d) cot ψ$
or $a c_{1} = (a + d) c_{2} = (a + 2 d) c_{3}$
Dividing by $c_{1} c_{2} c_{3}$ , we get
$\frac{a}{c_{2} c_{3}} = \frac{a + d}{c_{3} c_{1}} = \frac{a + 2 d}{c_{1} c_{2}} = λ$ say
Since $N^{r} s$ are in $A . P .$ , hence $D^{r} s$ are also in $A . P .$
or $cot ϕ, cot ψ, cot ψ, cot θ, cot θ, cot ϕ$ are also in $A . P .$

Suggest Corrections

Similar questions

Q. The angle of elevation of a cliff from fixed point is

θ

. After going up a distance of

k

meters towards the top of the cliff at are angle of

ϕ

, it is found that the angle of elevations is

α

. Show that height of a cliff is

\frac{k (cos ϕ - sin ϕ cot α)}{cot θ - cot α}

Q. Fill in the blanks
The angle of elevation of the top of a tower from a point

A

on the ground is

θ

and that from

B

ϕ

. If

A B = 100

metres and

A B

is perpendicular to the line joining

A

with the foot of the tower, then the height of the tower is ________________.
Given

cot θ = 3 / 10

and

cot ϕ = 1 / 2

From a window (h metres high above the ground) of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are $θ$ and $ϕ$ respectively. Show that the height of the opposite house is $h (1 + t a n θ c o t ϕ)$ metres [3 MARKS]