Question

$\huge \mathfrak \green{❥Question}$
From an aeroplane vertically above a straight horizontal road, the angle of
depression of two consecutive kilometer stones on opposite sides of the aero
plane are observed to be 60° and 30°. Show that height of aero plane above the

road is km.

[ Class 10 ]
✖ Kindly don't spam ✖​

Answer 1

Hey mate,

Let B and C be the two consecutive mile stones.

∴ BC = BD + CD = 1miles

Let the height of the aeroplane AD = Hmiles

⇒ In △ABD , tanα= BDAD ........ tan (Θ) =

Opposite

---------------

Adjacent

⇒ tanα= BD

----

h

⇒ BD = tanα

------ -------- ( 1 )

h

⇒ In △ACD, tan β = CD

----

AD

⇒ tanβ = CD

----- .......... tan(Θ) = Adjacent

-----------

Opposite

⇒ CD = tanβ

----- -------- ( 2 )

h

⇒ BC = BD + CD = h h

----- + ------

tanα tanα

⇒ BC = h 1 1

( ----- + ------ )

tanα tanα

⇒ 1 = h. tan α tan b

( ---------+-------- )

tan α tan b

∴ h = tan α tan b

( ----- + ------ )

tan a + tan b

⇒ Hence, height of the aeroplane is

tan α tan b

( ----- + ------ )

tan a + tan b

Hope it helps.....

$( Itz ❤Aakanksha❤ here! ) {}^{}$