Question

3. Angle of depression of a ship from the top of the light house of height 200m is 60°. Find the
distance between the ship and the light house.
4. From the
bot of a​

Answer 1

Answer:

Hello

Step-by-step explanation:

The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45 degree and 30 degree. If the ships are 200 m apart then what is the height of the light house?

Let top point of the light house A, a point B on the horizontal line through A in the plane of light house and the two ships .Hight of the light house h and its foot rest point is C , point focused of the nearer ship is D and 200 m apart is E .

angle BAE=AEC=30° ,

angle BAD=ADC=45°

AC/CE=Tan 30°=1/√3, CE/AC=√3

AC/CD= Tan 45°= 1 , CD/AC=1

(CE/AC) - (CD/AC) =√3–1

(CE-CD)/AC=0.732

200/AC=0.732

AC=200/0.732= 273.22 m

hight of the lighthouse =273.22 m

Answer 2

Answer:

h=100(3+1)

Step by step explanation:

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