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xz_007 [3.2K]
3 years ago
15

What conclusion can you draw about angles of elevation for parasailing boats traveling at the same speed?

Mathematics
1 answer:
melamori03 [73]3 years ago
6 0

Question:

A boat is travelling at 30 mph has  a 400 ft. tow line results in the height of the rider in the parasail above the water level of 300 ft.

a) Draw a labelled diagram of the situation

b) Determine the angle of elevation of the parasail rider

c) Parasailing boats traveling at the same speed will have the same angle of elevation

Answer:

a) Please find the attached drawing of the parasail boat created with MS Visio

b) The angle of elevation of the parasail rider from the boat is approximately 48.6°

Step-by-step explanation:

a) Please find the labelled diagram of the parasailing boat created with MS Visio

b) sing trigonometric ratios, we have;

sin(\theta) = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}

The opposite leg = The height of the parasail rider above water = 300 ft.

The hypotenuse = the length of the tow line = 400 ft.

θ = The angle of elevation of the parasail rider

\therefore sin(\theta) = \dfrac{300 \, ft.}{400 \, ft.} = 0.75

θ = Arctan(0.75) ≈ 48.6°

The angle of elevation above the horizontal of the parasail rider from the boat, θ ≈ 48.6°

c) From the construction of the drawing and the derivation of the angle of elevation given only the length of the tow line and the height given to the parasail rider by the speed of the both,

Parasailing boats traveling at the same speed, having the same length of tow line, will have the same angle of elevation, provided other factors that have an effect on the angle of elevation are the same

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Answer:

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b. One solution.

Step-by-step explanation:

Given the system of equations:

a. 2x-4y=12

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b. 2x-4y=12

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To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

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Let the system of equations be:

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a. 2x-4y=12 OR 2x-4y-12=0

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\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}

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Kindly refer to the images attached for the graphical representation of the given system of equations.

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