Question

Two ships are sailing in the sea on the
two sides of a lighthouse. The angles of
elevation of the top of the lighthouse as
observed from the ships are 30° and 45°
respectively. If the lighthouse is 100 m
high, the distance between the two ships​

Answer 1

Answer:

Let AB be the lighthouse and C and D be the positions of the ships.

Height and Distance mcq solution image

Then, AB = 100m, ∠ACB = 30° and ∠ADB = 45°

ABAC=tan30∘=13–√

⇒AC=AB×3–√=1003–√m

ABAD=tan45∘=1

⇒AD=AB=100m

∴ CD = (AC+AD) = (100√3 +100)

= 100(√3 +1) = 100(1.73+1) =100 × 2.73 = 273m

Step-by-step explanation:

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Answer 2

Answer:

height of lighthouse = 100m

Distance between ship A and lighthouse

tan45⁰ = 100/distance of A

1 =100/x

x=100m

Distance between ship B and lighthouse

tan30⁰ = 100/distance of B

1/1.732 = 100/y

y = 173m

Distance between both ships

173 - 100

73m