Question

two ships are sailing on see the author of the Lighthouse the angle of depression the ships are formed of the top of a Lighthouse 60 and 45 degree respectively if the distance between the ship is 200 root 3+1 upon root 3 find the find the height of lighthouse

Answer 1

Answer:

200 m

Step-by-step explanation:

Refer the attached figure. Let P and Q are two ships and AB is the lighthouse. Given that

$PQ=\frac{200(\sqrt3+1)}{\sqrt3}$

We need to find AB.

Let BQ = x

$PB=\frac{200(\sqrt3+1)}{\sqrt3}-x$

In ΔABQ

tan 45° = AB/BQ     [∵ tanФ = Opposite side/Adjacent Side]

1 = AB/x                    [∵ tan 45° = 1]

AB = x --------- ( i )

Now, in ΔABP

tan 60° = AB/PB

Putting tan 60° = √3

$\sqrt3 =\frac{AB}{\frac{200(\sqrt3+1)}{\sqrt3}-x}$

$\sqrt3(\frac{200(\sqrt3+1)}{\sqrt3}-x) =AB$

Putting AB = x    [from eq (i)]

${200(\sqrt3+1)}- {\sqrt3}x =x$

${200(\sqrt3+1)} =x+ {\sqrt3}x$

$x(\sqrt3+1)=200(\sqrt3+1)$

x = 200

∵ AB = x   [ from eq (i)]

∴ AB = 200 m

Hence, height of lighthouse is 200 m