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. 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) 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. 2 After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(root 3 - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower
  • 1 answers

Kavana Tn 3 months, 4 weeks ago

i)let x be the distance travelled by boat Angle of depression =30 degree Tan 30°=240/x 1/root 3=240/x x=240 root 3 Therefore distance travelled by boat is 240 root 3 m. ii) now angle of depression let be theta Distance of boat is reduced by 240(root3-1)m Let new distance travelled by boat be y Difference in distance is given Earlier distance - new distance =difference i.e 240root3 - y = 240(root 3-1) We get y=240 Tan theta =opp/adjacent Tan theta=240 i.e height of tower/ 240 i.e distance travelled Tan theta=1 Tan theta = Tan 45° Therefore theta=45° Hence the new angle of depression is 45 degree ( corresponding figure u can check here??)

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