A boat heading out to sea starts out at Point AA, at a horizontal distance of 734 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 14degrees ∘ . At some later time, the crew measures the angle of elevation from point BB to be 6degrees ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Question
A boat heading out to sea starts out at Point AA, at a horizontal distance of 734 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 14degrees ∘ . At some later time, the crew measures the angle of elevation from point BB to be 6degrees ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Solution
To solve this problem, we can use the tangent of the angles of elevation, which is the ratio of the opposite side (the height of the lighthouse) to the adjacent side (the horizontal distance from the lighthouse).
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First, we can find the height of the lighthouse using the tangent of the angle of elevation from point A.
tan(14°) = height / 734 feet height = tan(14°) * 734 feet
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Then, we can find the total horizontal distance from the lighthouse to point B using the height of the lighthouse and the tangent of the angle of elevation from point B.
tan(6°) = height / distance_B distance_B = height / tan(6°)
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Finally, we can find the distance from point A to point B by subtracting the horizontal distance from the lighthouse to point A from the total horizontal distance from the lighthouse to point B.
distance_AB = distance_B - 734 feet
Remember to use a calculator to find the tangent of the angles and to round your answer to the nearest foot if necessary.
Similar Questions
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