Quote:
A boat, stationed at the North of a 300-feet high lighthouse, is making an angle of 30° with the top of the lighthouse. Simultaneously, another boat, stationed at the East of the same lighthouse, is making an angle of 45° with the top of the lighthouse. What will be the shortest distance between these two boats? Assume both the boats are of negligible dimensions.
Step 1: Understanding the questionUsing the relation of special right angle triangle 30° : 60° : 90° as x : x√3 : 2x
The boat stationed at the North of a 300-feet high lighthouse, making an angle of 30° with the top of the lighthouse, is
300√3 feet away from the lighthouse (opposite to 60°).
Using the relation of special right angle triangle 45° : 45° : 90° as x : x : x√2
The boat stationed at the East of the same lighthouse, is making an angle of 45° with the top of the lighthouse, is
300 feet away from the lighthouse (opposite to 45°).
Step 2: CalculationThe two boats are making right angle with each other, hence using Pythagorean theorem to find distance between them.
Distance between the two boats = √[\((300√3)^2 + (300)^2\)] = 300 * √[\((√3)^2 + 1^2\)] = 300*2 = 600 feet
D is correct _________________
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