Question

a man is standing on the deck of a ship which is 25m above water level. he observes the angle of elevation of the top of a light house as 60degree and the angle of deviation of the base of the height house at 45degree, calculate the height of the light house.

Answer 1

height of light house is 25(√3+1)

Answer 2

Answer:

25(√3 + 1) meters

Step-by-step explanation:

Let AB represents the light house ( A shows its top ), BC represents the sea level and D represents the position of the man,

By the below diagram,

In triangle DCB,

$tan 45^{\circ}=\frac{CD}{BC}$

$1=\frac{25}{BC}\implies BC = 25\text{ m}$

⇒ ED= 25 meters,

Now, in triangle DAE,

$tan 60^{\circ}=\frac{AE}{ED}$

$\sqrt{3}=\frac{AE}{25}$

$\implies AE = 25\sqrt{3}$

Hence, the height of lighthouse, AB = AE + EB = 25√3 + 25 = 25(√3 + 1) meters