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Solution


Q.

Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS, a radio navigation system, helps to locate our position on earth with the help of satellites. A guard, stationed at the top of a 240 m tower, observed an unidentified boat coming towards it. A clinometer or inclinometer is an instrument used for measuring angles or slopes (tilt). The guard used the clinometer to measure the angle of depression of the boat coming towards the lighthouse and found it to be 30°.

(Lighthouse of Mumbai Harbour — Picture credits: Times of India Travel)

 

(i) Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower
1 2403 m  
2 2402 m  
3 -2403 m  
4 2353 m  

Ans.

(1)

Let TR be the tower, observer at point T, P be the boat and PR = x.

From the figure,

 ∠MTP=∠TPR=30° tan30°=TRPR

13=240x⇒x=2403m

Hence, the boat is 2403 m