Question

A boat heading out to sea starts out at Point AA, at a horizontal distance of 1032 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 15degrees

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. At some later time, the crew measures the angle of elevation from point BB to be 6degrees
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. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

≈ 1598.9
use tan

Explanation: u dont need one lil bro

Answer 2

To find the distance from point AA to point BB, use trigonometry to calculate the heights of the lighthouse at the two points, and then subtract the heights to find the distance. We get 161.5 feet.

Step-by-step explanation:

To find the distance from point AA to point BB, we can use the concept of trigonometry and the tangent function.

The tangent of an angle is equal to the opposite side divided by the adjacent side.

In this case, the opposite side is the height of the lighthouse and the adjacent side is the horizontal distance from the boat to the lighthouse.

Using the given angle of elevation of 15° at point AA, we can calculate the height of the lighthouse by multiplying the horizontal distance (1032 feet) by the tangent of the angle.

So, height = 1032 feet × tan(15°)

= 268.4 feet.

Similarly, we can calculate the height at point BB using the given angle of elevation of 6°.

The height at point BB = 1032 feet × tan(6°)

= 106.9 feet.

Finally, to find the distance from point AA to point BB, we can subtract the heights at the two points.

Distance = 268.4 feet - 106.9 feet

= 161.5 feet.