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Evgen [1.6K]
3 years ago
11

You are on a boat in the ocean at point A. You locate a lighthouse at point D, beyond the line of sight of the marker at point C

. You travel 90 feet west to point b and then 36 feet south to point C. You travel 100 feet more to arrive point E, which is due east of the lighthouse. What is the distance from point E to the lighthouse?

Mathematics
1 answer:
kicyunya [14]3 years ago
6 0

Answer: The distance from point E to the lighthouse = 250 feet

Step-by-step explanation:

Since, after making the diagram of this situation,

We get two triangles ABC and CED,

In which AB = 90 feet, BC = 36 feet and CE = 100 feet,

Now,

\angle ACB\cong \angle ECD        ( Vertically opposite angles )

\angle ABC\cong \angle DEC         ( Right angles )

By AA similarity postulate,

\triangle ABC\sim \triangle DEC

By the property of similar triangles,

\frac{AB}{ED}=\frac{BC}{EC}

\frac{90}{ED}=\frac{36}{100}

9000=36DE

250=DE

Since, point D represents the lighthouse.

Hence, the distance from point E to the lighthouse = 250 feet

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