Question

NEED HELP ASAP!!
A boat is heading towards a lighthouse, whose beacon-light is 114 feet above the water. The boat's crew measures the angle of elevation to the beacon, 5º. 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.

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.

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