Question

Please give me step by step explanation.. ​

Answer 1

Let D and C be given ships and AB be the lighthouse.

Let Height of light house is AB=h

In △BAC, we have:

tan45∘=BCAB

1=BCAB ⟹AB=BC

so, BC=h                 ... (1)

 

In triangle ADB,

tan30∘=BDAB

31=BC+200h

31=h+200h            [Using (1)]

h+200=h3

h(3−1)=200

h=3−1200 m

OR,

By rationalization and simplification, we get,

h=100(3+1) m

Answer 2

Answer:

Interesting!

See the figure, I used ms paint.

Now, Let CA=x m.

Lenght of CB=CA+AB = (x+200) m.

• Let's take ΔDCA.

tan 45°=1

tan 45°⇒ Perpendicular/base ⇒ DC/AC

DC/x=1

x=DC

• Let's take ΔDCB

tan 30° = 1/√3.

tan 30°⇒ Perpendicular/base⇒ DC/CB

1/√3=DC/(200+x)

200+x=√3(DC) [Substitute the value of x=DC)

200+DC=√3(DC)

200=√3DC-DC

200=DC(√3-1)

DC={200/(√3-1)}m

Rationalise the fraction.

DC=100(√3+1)m.

HOPE THIS HELPS :D