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svp [43]
2 years ago
6

A boat is heading towards a lighthouse, whose beacon-light is 126 feet above the water. From point AA, the boat’s crew measures

the angle of elevation to the beacon, 6^{\circ} ∘ , before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 22^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Mathematics
1 answer:
vredina [299]2 years ago
6 0

Using the slope concept, it is found that the distance from point A to point B is of 887 feet.

<h3>What is a slope?</h3>

The slope is given by the <u>vertical change divided by the horizontal change</u>.

It's also the tangent of the angle of depression.

In this problem, the vertical change is of 126 feet.

At point A, the angle is of 6º, while the horizontal position is of x_A, hence:

\tan{6^\circ} = \frac{126}{x_A}

x_A = \frac{126}{\tan{6^\circ}}

x_A = 1198.8

At point B, the angle is of 22º, while the horizontal position is of x_B, hence:

\tan{22^\circ} = \frac{126}{x_B}

x_B = \frac{126}{\tan{22^\circ}}

x_B = 311.9

Hence, the distance in feet is of:

d = x_A - x_B = 1198.8 - 311.9 \approx 887

More can be learned about the slope concept at brainly.com/question/18090623

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To make a sports drink for the football team, Jaylen filled \dfrac9{10}
Scilla [17]

The total gallons of sports drink Jaylen made using 9/10 of a large cooler with water and 6 cups of sports drink concentrate is 3.75 gallons

<h3>Total gallons</h3>

  • Water in the large cooler = 9/10

Space remaining = 1 - 9/10

= 10-9 / 10

= 1/10

1/10 = 6 cups

  • Total gallons of sport drink = x

6 cups / total = 1/10

6 × 10 = total × 1

60 cups = total

Cups to gallons:

16 cups = 1 gallon

Total gallons of sport drink, x = 60 cups / 16

= 3.75 gallons

Complete question:

To make a sports drink for the football team, Jaylen filled 9/10 of a large cooler with water. Then, he filled the remaining space with 6 cups of sports drink concentrate. How many gallons of sports drink did Jaylen make?

Learn more about total gallons:

brainly.com/question/26007201

#SPJ1

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nignag [31]

sin(x) = opp/hyp
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tan(x) = opp/adj

sin(x) = 3.9/8.1
sin(x) = 0.481

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Completely Factoring<br> 3x2 – 10x – 8
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Step-by-step explanation:

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