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A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 9 degrees. 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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oladayoademosu

The horizontal distance of the boat from the lighthouse is 17.58 ft.

The required triangle

The height of the lighthouse beacon, h the line of sight of the boat to the top of the beacon and the horizontal distance of the boat from the lighthouse form a right-angled triangle with opposite side, the height of the lighthouse and adjacent side the horizontal distance of the boat from the lighthouse, D.

The horizontal distance of the boat from the lighthouse

Since the angle of elevation of the beacon is 9°, we have using trigonometric ratios that

tan9° = h/D

So, D = htan9°

Since h = 111 ft,

D = 111tan9°

D = 111 × 0.1584

D = 17.58 ft

So, the horizontal distance of the boat from the lighthouse is 17.58 ft.

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