Question

please give me correct answer I am studing for class 10 board don't give wrong comments​ of 13 question

Answer 1

Explanation:

this is your answer

Step by step explanation

Answer 2

Explanation:

Let AB be the lighthouse. The height (h) of the lighthouse from the sea level is AB=h=75 m.

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

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

Lat the distance be x m (see figure).

= CD = x m

In triangle ABC,

Perpendicular. AB. 75

tan 45°= ---------------------- = ------- = -----

Base. BC. BC

As we know tan 45°= 1

= BC = 75 m

Now in triangle ABD

Perpendicular. AB

tan 30° = ----------------------- = --------

Base. BD

As we know tan 30° = 1

-----

√3

So subtract this value in above equation we have,

= 1. 75

----- = ---------

√3. BD

= BD = 75√3 m

So from figure CD = BD - BC

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

Therefore, CD = 75√3 - 75

= x = 75 (√3 - 1) m

So, the distance between two ships is 75 (√3 - 1) meter.

So, this is the required answer.

Note : Whenever we face such height and distance problems the key point is about the basic understanding of the simple trigonometric ratios and their formulas like that is sin, cos and tan. The application of this tangonometric ration will set you on the right track to get the required answer.

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