MATHEMATICS MIDDLE SCHOOL

The angle of depression of a boat at sea from a 100 foot lighthouse is 20 degrees. Find the distance to the boat.not sure how to solve this..

Answers

Answer 1
Answer:

Answer:

As per the statement:

The angle of depression of a boat at sea from a 100 foot lighthouse is 20 degrees.

We draw the figure for this problem as shown below:

Height of the lighthouse(BC) = 100 foot

Angle of depression = 20 degrees.

Since, angle of depression is equal to the angles of elevation

i.e, \angle DCA = \angle CAB = 20^(\circ)

using tangent ratio:

\tan \theta = \frac{\text{opposite side}}{\text{adjacent side}}

Here,

Opposite side = BC = 100 foot

Adjacent side = AB

Angle of elevation: \theta = 20^(\circ)

Substitute these to solve for AB:

\tan 20^(\circ) = \frac{100}{\text{AB}}

or

\text{AB} =(100)/(\tan 20^(\circ))

\text{AB} =(100)/(0.36397023426)

Simplify:

AB = 294.375362123 foot

Therefore, the distance to the boat approximately is 294.4 foot
Answer 2
Answer:

Final answer:

By using the tangent function with the given height of the lighthouse and the angle of depression, we can solve for the distance to the boat, which is approximately  274.1 feet.

Explanation:

In this scenario, we can use trigonometry to find the distance to the boat. Since we know that the lighthouse is 100 feet high and the angle of depression is 20 degrees, this fits the scenario for a tangent function, where tangent of an angle equals the opposite side divided by the adjacent side.

Setting up our function, we get tan(20) = 100/ distance to the boat. Since we want to find the distance to the boat, we can rearrange the equation to be distance to the boat = 100 / tan(20).

Doing this calculation, we find that the distance to the boat is approximately 274.1 feet.

Learn more about Trigonometry here:

brainly.com/question/11016599

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What is 15 (x+20)Please help me in any way you can
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Answers

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