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A boat is heading towards a lighthouse, whose beacon-light is 139 feet above the water. The boat's crew measures the angle of elevation to the beacon,
11^(@). 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.

A boat is heading towards a lighthouse, whose beacon-light is $139$ feet above the water. The boat's crew measures the angle of elevation to the beacon, $11^{\circ}$ . 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. A boat is heading towards a lighthouse, whose beacon-light is

139

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

11^{\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.

Use tangent function: Use the tangent function because we have the angle of elevation and the opposite side (height of the lighthouse) and we want to find the adjacent side (horizontal distance). $\newline$ $\tan(11^\circ) = \frac{\text{opposite}}{\text{adjacent}}$
Plug in values: Plug in the known values. $\newline$ $\tan(11^\circ) = \frac{139}{\text{adjacent}}$
Solve for adjacent side: Solve for the adjacent side. $\text{adjacent} = \frac{139}{\tan(11°)}$
Calculate adjacent side: Use a calculator to find $\tan(11°)$ and then divide $139$ by this value. $\newline$ $\text{adjacent} \approx \frac{139}{0.19438}$
Find horizontal distance: Perform the division to find the horizontal distance. $\text{adjacent} \approx 715.35$
Round to nearest hundredth: Round the answer to the nearest hundredth of a foot. $\newline$ adjacent $\approx 715.35$ feet

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