Question

Two ships are sailing in the sea on the either side of the lighthouse, the angles of depression of two ships as observed from the top of the lighthouse are 60 and 45 respectively. If the distance between the ships is 200 31 3 + metres, find the height of the lighthouse

Answer 1

Answer:200 CM

Step-by-step explanation:

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Answer 2

Answer:

• A, B are the position of two ships.CD - Lighthouse.

• Angle of depression of the First ship A from the top of the Lighthouse ∠X'DA = 60°.

• Angle of depression of the second ship But from the top of an lighthouse is ∠ XDB = 45°.

Distance between the ships

AB = 200 (√3 + 1 / 3) m

In the right angle triangle ADC,

tan 60° = CD / AC

AC = CD / tan 60°

AC = CD / √3 ------> EQUATION 1

In the right angle triangle BDC,

tan 45° = CD / BC

1 = CD / BC

BC = CD -------> EQUATION 2

Adding equation 1 and 2 , we get

AC + BC = CD / √3 + CD

AB = CD (1/√3 + 1)

200 ( √3 + 1 /√3) = CD (1 + √3 / √3)

CD = 200

∴ Height of the lighthouse = 200m.

Step-by-step explanation:

@GENIUS