Question

A boat rows away from a cliff of height 120 m. From the top of the cliff the angle of depression of the boat changes from 60° to 45° in 2 minutes. Which of the following is the speed of the boat?

20(3−3√) m/hr

20(1−3√) m/hr

1200(1−13√) m/hr

1200(3−3√) m/hr

Answer 1

Answer:

Let AB be the light house of 120m. and c be the boat.

Let ∠DAC=15∘ (Angle of depression)

In ΔABC

tan15∘=ABBC

tan(45∘−30∘)=ABBC.

⇒tan45∘−tan30∘1+tan45∘tan30∘=120BC

⇒3–√−13–√+1=120BC ltbgt ⇒BC=120((3–√+1)23−1)=60(3+1+23–√)

=60(4+2×1.73)

=60×7.46=447.6m≅444mation:

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