Question

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

Answer 1

Step-by-step explanation:

in triangle ABC

Tan40= AB/BC

=BC= AB/Tan40

BC=80/0.8391 = 95.34 m

in triangle ABD, tan30=AB/BD

=  BD = AB/tan 30˚ = 80/0.5774

=138.55 m

the distance between the two ships is

DC = BD – BC

= 138.55 – 95.34

= 43.21 m = 43 m

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