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Question
A boat is heading towards a lighthouse, whose beacon-light is 148 feet above the water. The boat's crew measures the angle of elevation to the beacon,
8^(@). What is the ship's horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.

Question $\newline$ A boat is heading towards a lighthouse, whose beacon-light is $148$ feet above the water. The boat's crew measures the angle of elevation to the beacon, $8^{\circ}$ . What is the ship's horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.

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Pythagorean theorem

Full solution

Q. Question

\newline

A boat is heading towards a lighthouse, whose beacon-light is

148

feet above the water. The boat's crew measures the angle of elevation to the beacon,

8^{\circ}

. What is the ship's horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.

Identify Relationship: Identify the relationship between the angle of elevation, the height of the lighthouse, and the horizontal distance.
Convert to Radians: Convert the angle of elevation to radians and calculate the tangent.
Set Up Equation: Set up the equation using the tangent value and the height of the lighthouse.
Solve for $x$ : Solve for $x$ , the horizontal distance.

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