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Rina8888 [55]
3 years ago
9

The Son of Beast roller coaster at Kings Island in Cincinnati, Ohio is the tallest wooden roller coaster in the world. The highe

st point of the coaster is 66 m high. What is the angle of elevation, to the nearest degree, to the top of the coaster from a point on the ground 72 m *
Mathematics
1 answer:
aliya0001 [1]3 years ago
3 0

Answer:

43 °

Step-by-step explanation:

In the statement they mention the height and in addition to that the horizontal distance where a right triangle is formed, therefore we can apply a trigonometric ratio to calculate the angle, in this case it is the tangent, which relates the two legs of the angle:

Tan A ° = opposite / adjacent

opposite = 66, adjacent = 72, replacing we have:

Tan A ° = 66/72 = 0.9166

A ° = arc tan (0.9166)

A ° = 42.51

That is, the angle of elevation is 43 °

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URGENT! PLEASE HELP.
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The distance BC from Tower 2 to the plane will be 14,065.5 ft and the height of the plane from the ground will be 5,720.9 ft.

<h3>What is a right-angle triangle?</h3>

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

A plane is located at C on the diagram.

There are two towers located at A and B.

The distance between the towers is 7600 feet and angles of elevation are given.

Then in the right-angle triangle ΔADC, we have

\rm \tan 16 = \dfrac{H}{7600 + X}\\\\\\H = 0.2867(7600 +X)\\\\\\H = 0.2756\ X + 2179.2649 ...1

Then in the right-angle triangle ΔBDC, we have

\rm \tan24 = \dfrac{H}{ X}\\\\\\H = 0.4452\ X ...2

From equations 1 and 2, we have

0.4452X = 0.2756 X + 2179.2649

0.1696X = 2179.2649

            X = 12849.439 ≅ 12,849.4 ft

Then the distance BC from Tower 2 to the plane will be

\rm BC = \dfrac{12849.4}{\cos 24}\\\\\\BC = 14065.5 \ ft

Then the height of the plane from the ground will be

\rm H = 12849.4 \times  \tan 24 \\\\\\H = 5720.9 \ ft

The figure is shown below.

More about the right-angle triangle link is given below.

brainly.com/question/3770177

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2 years ago
which of the following is the missing reason? Statements Reasons three halves times x plus 5 equals negative 4 Given 3x + 10 = −
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Answer:

The missing reason is Subtraction Property of Equality.

Step-by-step explanation:

\frac{3}{2}x+5=-4    ⇒ (Given)

On Solving we get;

Multiplying 2 on both side we get;

2(\frac{3}{2}x+5)=-4\times2\\\\2\times \frac{3}{2}x+5\times 2=-4\times 2

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Now Subtracting Both side by 10 we get;

3x+10-10=-8-10

3x = -18     ⇒ (Subtraction Property of Equality)

Now Dividing both side by 3 we get;

\frac{3x}{3} = \frac{-18}{3}

x=-6        ⇒ (Division Property of Equality)

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<h2>Verbal Phrase to Mathematical Phrase</h2><h3>Answer:</h3>

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The quotient of a number and 6 is \frac{n}{6}\\.

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And it tells us that it is 15 so it must be 10 +\frac{n}{6} = 15\\

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3 years ago
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