Question

14. As observed from the top of a 80 m tall lighthouse,
the angles of depression of two ships on the same side
of the light house in horizontal line with the base are
30° and 40° respectively. Find the distance between
the two ships. Give your answer correct to the nearest
metre.
​

Answer 1

Answer:

43 meter

Step-by-step explanation:

In △ABC,

tan 40˚ = AB/BC

⇒ BC = AB/tan 40˚

BC = 80/0.8391 = 95.34 m

In △ABD, tan 30˚ = AB/BD

⇒ BD = AB/tan 30˚ = 80/0.5774

= 138.55 m

Distance between two ships

DC = BD – BC

= 138.55 – 95.34

= 43.21 m = 43 m

Answer 2

Distance between the ships is 43.22m

Given

• 80 m tall lighthouse
• angles of depression of two ships 30° and 40° respectively

To find

• the distance between
• the two ships

Solution

we are provided with the angle of depressions of two ships and are asked to find the distance between the two ships.

from the figure, considering the triangle ADC,

tan40 = DC/AD

or, tan40 = 80/AD

or, AD = 80/tan40

considering the triangle BDC,

tan30 = DC/DB

or, tan 30 = 80/DB

or, DB = 80/tan30

or, DB = 80√3

now the distance between the ships is given by,

AB ie,

AB = DB - AD

or, AB = 80√3 - 80/tan40 ( from above)

or, AB = 138.56 - 95.34

or, AB = 43.22 m

Therefore, the distance between the ships is

43.22m