Question

if the angle of elevation of a balloon from two consecutive kilometre-stones along a road are 30 and 60 degree ?

plz clarify this line

Answer 1

Answer:

The baloon is flying at a height of 0.866 km above the road

Step-by-step explanation:

Let A be the position of the baloon.

Let C and D be the consecutive milestones.

In right Δ ABC,

$tan\:60=\frac{AB}{BC}$

$\sqrt3=\frac{AB}{BC}$

$BC=\frac{AB}{\sqrt3}$.........(1)

In right Δ ABD,

$tan\:30=\frac{AB}{BD}$

$\frac{1}{\sqrt3}=\frac{AB}{BC+CD}$

$\frac{1}{\sqrt3}=\frac{AB}{BC+1}$

using (1) we get

$\frac{1}{\sqrt3}=\frac{AB}{\frac{AB}{\sqrt3}+1}$

$\frac{1}{\sqrt3}=\frac{\sqrt{3}AB}{AB+\sqrt{3}}$

$AB+\sqrt{3}=3AB$

$3AB-AB=\sqrt{3}$

$2AB=\sqrt{3}$

$AB=\frac{\sqrt{3}}{2}$

$AB=\frac{1.732}{2}$

$AB=0.866\:km$

Therefore, the baloon is flying at a height of 0.866 km above the road.