Question

As observed from the top of a 150 m tall eight house,
the angles of depression of two shibe abboaching it are
30 and 60. If ope ship is directly behind the other.
Find the dischce between the two stipe
,

Answer 1

Answer:

Mark as Brainliest answer if you like it

Step-by-step explanation:

Let AB be the light house. The height (h) of the lighthouse from the sea level is AB = h = 150 m.

Now the angle of depression of the ships is 30 degree and 45 degree and the one ship is exactly behind the other one on the same side of the light house (see figure).

Now we have to find out the distance between the ships.

Let the distance be x m (see figure).

⇒CD=x meter.

In triangle ABC,

tan450=PerpendicularBase=ABBC=150BC

As we know tan450=1

⇒BC=150 meter.

Now in triangle ABD

tan300=PerpendicularBase=ABBD

As we know tan300=13–√

So substitute this value in above equation we have,

⇒13–√=150BD

⇒BD=1503–√ meter.

So from figure CD = BD – BC

So, substitute the values of BD and BC in above equation we have

∴CD=1503–√−150

⇒x=150(3–√−1) meter.

Now simplifying this we have,

⇒x=150(1.732−1)=150(0.732)=109.8 meter. [∵3–√=1.732]

So, the distance between two ships is 109.8 meter.

So, this is the required answer.

Note: Whenever we face such type of height and distance problems the key concept is to have a diagrammatic representation of the information provided in the question as it helps in understanding the basic geometry of the figure. Use the concept of basic trigonometric ratios in respective triangles to get the answer.