A boat is 3000m out at sea.The angle of depression of the boat from the top of a lighthouse is 15.7°.

Question

i)Find Its height of the lighthous.

ii)If the boat now sails a further 2000m out to sea, find the angle of elevation of the top of the lighthouse from the boat.

Comments

Thank you very much

Answer 1

let h is the hight of the lighthouse. we have tan15.7 = h/3000 -->>>  h=3000tan15.7 and since

tan15.7 = 0.28108  we have  h=3000 x 0.28108 = 843.26 m (very high building I must say)

now let e is the elevation angle. we have tan(e)=h/5000 --->>> tan(e) = 843.26/5000 = 0.16865

so the elevation angle is the angle having tan value = 0.16865

Comments

Help me With a diagram

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AB=h = heigh of light house, BC = 3000m, CD = 2000m, BD = 5000, d=depression angle

e = elevation angle