Question

The angle of depression of two ships from the top of a light house are 45 and
the ships are 200 m apart, find the height of the light house.​

Answer 1

Answer:

Step-by-step explanation:

See the pic below for solution.

U didn't write the value of second angle and hence I solved the ques by considering it to be 30°. In case it is 60 then replace the value.

Answer 2

Question :-

The angle of Two ships from the top of a light house are 45° and 30° towards east .if the ships are 200m a part,the height of light house is

Given :-

• angle of Two ships from the top of a light house are 45° and 30° towards east
• if the ships are 200m.

Fine :-

• height of he light house ?

Solution :-

Let

• The height of the light house be 'h' m

→ in ∆ ABC ,

→ ∠B = 90°

$\sf⇒ \dfrac{AB}{AC}= tan45° \\ \sf ⇒ \dfrac{h}{x}=1$ ( tan 45° = 1 )

$\sf ⇒ \dfrac{h}{x}=\dfrac{1}{1}$ { on cross multiply }

$\sf ⇒ x = h$_____(1)

→ in ∆ ABD

→ ∠B = 90°

$\sf ⇒ \dfrac{AB}{BD}=tan30°\\ \sf ⇒ \dfrac{h}{x+200}=\dfrac{1}{\sqrt{3}}$ {tan 45° = 1/√3 }

$\sf ⇒ h \sqrt{3}=x+200$______(2)

• Putting the value of x in eqⁿ(2)

→ h√3 = h + 200

→ h√3 - h = 200

→ h ( √3 - 1 ) = 200

→ h = 200/√3 - 1. { √3 = 1.733 }

→ h = 200/1.732 - 1

→ h = 200/0.732

→ h = 273.2 metre

Hence

• The height of light house is 273 . 2 metre