Question

as observed from the top of 60 M high Lighthouse from the sea level the angle of depression of two ships are 30° and 45° if one ship is exactly behind the other on the same side of the Lighthouse find the distance between the two ships

Answer 1

Answer:

43.92 m

Step-by-step explanation:

See the figure in attachment .

D and C are the two ships and they are separated by the distance DC .

Let DC be x .

The height of the lighthouse is given 60 m .

Hence AB = 60 .

Use √3 as 1.732 .

Also use tan Ф = ( side opposite to Ф ) / ( side adjacent to Ф )

Use tan 45 = 1 .

Use tan 30 = 1/√3 .

∠ACB = 30°

∠ADB = 45°

In Δ ABD ,

tan 45° = AB /BD

⇒ tan 45° = 60/BD

⇒ 1 = 60/BD

⇒ BD = 60

From the figure we have BD + DC = BC

⇒ 60 + x = BC

In Δ ABC ,

tan 30° = AB/BC

⇒ 1/√3 = 60 / ( 60 + x )

⇒ 60 + x = 60√3

⇒ x = 60√3 - 60

⇒ x = 60 ( √3 - 1 )

⇒ x = 60( 1.732 - 1 )

⇒ x = 60 × 0.732

⇒ x = 43.92

The distance between the ships is 43.92 m .

Answer 2

ANSWER:----------

IN THE ATTACHMENT:-

43.92

hope it helps:---

T!—!ANKS!!!