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Sagot :
The distance of the ship from the lighthouse can be determined using
trigonometric ratios.
- The ship's horizontal distance from the lighthouse is approximately 1,303.03 feet.
Reasons:
The given parameters are;
The height of the beacon-light above the ground = 114 feet
The angle of elevation to the beacon measured by the boat crew = 5°
Required:
The horizontal distance of the ship from the lighthouse
Solution:
The beacon-light that is seen by the boat crew, the height of the beacon light, and the horizontal distance of the ship from the lighthouse form a right triangle.
Therefore, we have;
[tex]\displaystyle tan (\theta) = \mathbf{ \frac{Opposite}{Adjacent}}[/tex]
[tex]\displaystyle tan(angle \ of \ elevation) = \mathbf{\frac{Height \ of \ beacon \ light}{The \ ship's \ horizontal \ distance \ from \ the \ lighthouse}}[/tex]
Which gives;
[tex]\displaystyle The \ ship's \ horizontal \ distance \ from \ the \ lighthouse= \frac{Height \ of \ beacon \ light}{tan(angle \ of \ elevation)}[/tex]
Therefore;
[tex]\displaystyle The \ ship's \ horizontal \ distance \ from \ the \ lighthouse= \frac{114 \ feet}{tan(5^{\circ})} \approx \mathbf{1,303.03 \ feet}[/tex]
The ship's horizontal distance from the lighthouse = 1,303.03 feet.
Learn more about angle of elevation here:
https://brainly.com/question/15821537
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