Heights and Distances Practice Test 1

Question : 19 of 40

Marks: +1, -0

A man is observing from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 60 m from the tower. After 5 seconds, the angle of depression becomes 30°. Find the speed of the boat, assuming that it is running in still water.

30 km/hr.
31.5 km/hr
33 km/hr
34 km/hr

Validate

Solution:

Let AB = h m be the height of the tower; C and D are the two points on the ground such that BC = 60 m; ∠ ACB = 45° and ∠ ADB = 30°
Now from right triangle ABC,

\tan 45°=h/60⇒1=h/60

∴h=60\m

Again from right triangle ABD;

\tan 30°=h/{x+60}⇒1/√3=60/{x+60}

⇒x+60=60√3

∴ x = 60 (1.73 – 1) = 43.8m
Hence, speed of boat

=43.8/5\m\/\s

=43.8/5×18/5≈ 31.5\km\/\hr

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