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tatiyna
2 years ago
13

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

he angle of depression to the boat is 14°52'. When the boat stops, the angle of depression is 45°10'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
Mathematics
1 answer:
tatyana61 [14]2 years ago
4 0

The boat's travel from when it was first noticed until it stopped is 554.89 ft.

<h3>What is trigonometry?</h3>

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.

From the given information we can draw a right-angle triangle.

14°52' = 14 + 0.86 = 14.86 degree

45°10' = 45 + 0.16 = 45.16 degree

In the right-angle triangle ACD

tan14.86 = 200/AC

AC = 753.772 ft

In the right-angle triangle DBC:

tan45.16 = 200/CB

CB = 198.886 ft

AB = AC - CB

AB =  753.772 ft - 198.886 ft

AB = 554.886 ≈ 554.89 ft

Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ1

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Simplified:  y^{3}-9y^{2}+27y-27

Step-by-step explanation:

Expanded: (y-3)(y-3)(y-3)

Simplified:

y^{2} -3y-3y+9(y-3)\\y^{2} -6y+9(y-3)

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ascending order:

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angle KML

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Question #1

Part A:
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The domain is 10.



Question #2

Part A:

(2,255)
(5,480)

Standard form is Ax + By = C

\sf Slope = \frac{y_2-y_1}{x_2-x_1} = \frac{480-225}{5-2} = \frac{255}{3} = \boxed{85}

Let's plug this into this form first:
y - y_1 = m(x-x_1)\\\\y -225 = 85(x-2)\\\\y - 225 = 85x - 170\\\\y = 85x + 55

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y = 85x + 55\\\\y - 85x + 55\\\\ -85x + y = 55\\\\ -1(-85x +y) = -1(55)\\\\\boxed{85x - y = -55}
What, which is in the box, is your final answer. :)

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\boxed{f(x) = 85x + 55}

Part C:
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