Question

as observed from the top of a 100m high light house from a sea level, the angles of depression of 2 ships are 30 and 45 degree .if one ship is exactly behind the other on the same side of the light house, then find the distance between the 2 ships and use root 3 =1.732

Answer 1

The answer is in photograph

Answer 2

Answer:

73.2 m

Step-by-step explanation:

Given :

Height of light house = 100 m

The angles of depression of 2 ships are 30 and 45 degree.

To Find: If one ship is exactly behind the other on the same side of the light house, then find the distance between the 2 ships

Solution :

Refer the attached figure

In ΔABC

AB = Height of tower = Perpendicular = 100 m

BC =  Base

∠ACB = 45°

We will use trigonometric ratio to find the length of  base :

$tan\theta = \frac{Perpendicular}{Base}$

$tan45^{\circ} = \frac{AB}{BC}$

$1 = \frac{100}{BC}$

$BC= 100$

In ΔABD

AB = Height of tower = Perpendicular = 100 m

BD = Base

∠ADB = 30°

We will use trigonometric ratio to find the length of  base :

$tan\theta = \frac{Perpendicular}{Base}$

$tan30^{\circ} = \frac{AB}{BD}$

$\frac{1}{\sqrt{3}} = \frac{100}{BD}$

$BD= \frac{100}{\frac{1}{\sqrt{3}}}$

$BD=100\sqrt{3}$

Use √3 = 1.732

⇒ BD= 100 * 1.732

⇒ BD = 173.2 m

Now we are required to find the distance between the 2 ships i.e. CD = BD-BC.

So,  CD = BD-BC.

CD = 173.2 m - 100 m

CD= 73.2 m

Thus the distance between the 2 ships is 73.2 m