Question

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Answer 1

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;

$\displaystyle tan (\theta) = \mathbf{ \frac{Opposite}{Adjacent}}$

$\displaystyle tan(angle \ of \ elevation) = \mathbf{\frac{Height \ of \ beacon \ light}{The \ ship's \ horizontal \ distance \ from \ the \ lighthouse}}$

Which gives;

$\displaystyle The \ ship's \ horizontal \ distance \ from \ the \ lighthouse= \frac{Height \ of \ beacon \ light}{tan(angle \ of \ elevation)}$

Therefore;

$\displaystyle The \ ship's \ horizontal \ distance \ from \ the \ lighthouse= \frac{114 \ feet}{tan(5^{\circ})} \approx \mathbf{1,303.03 \ feet}$

The ship's horizontal distance from the lighthouse = 1,303.03 feet.

Learn more about angle of elevation here:

brainly.com/question/15821537