Answered

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2. Calculate the distance MI for the length of the zipline cable. 3. Calculate the angle at which our zipliners will be descending toward the island . Safety regulations state that the angle at which a zipline cable meets the launching point cannot be smaller than 68 degrees . Please determine if we are in compliance with these regulations

2 Calculate The Distance MI For The Length Of The Zipline Cable 3 Calculate The Angle At Which Our Zipliners Will Be Descending Toward The Island Safety Regulat class=

Sagot :

right

[tex]\begin{gathered} AI)\text{ 400 ft} \\ MI)412.31\text{ f} \\ \text{angle = 76} \end{gathered}[/tex]

Explanation

Step 1

AI?

we have a rigth triangle

then

let

[tex]\begin{gathered} AB=side1 \\ AI=side\text{ 2} \\ IB=\text{ hypotenuse} \end{gathered}[/tex]

we can use the pythagorean Thoerem to find the missing vale

so

[tex]\begin{gathered} (AB)^2+(AI)^2=(BI)^2 \\ \text{replace} \\ 300^2+(AI)^2=500^2 \\ so \\ (AI)^2=500^2-300^2 \\ AI=\sqrt[]{500^2-300^2}=\sqrt[]{160000}=400 \\ AI=400 \end{gathered}[/tex]

Step 2

MI?

let

[tex]\begin{gathered} \text{angle}=x \\ \text{opposite side=100 m} \\ \text{adjacent side=400 m} \end{gathered}[/tex]

so, we need a function that relates those 3 values

[tex]\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]

replace

[tex]\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan x=\frac{400}{100} \\ \tan x=4 \\ \text{hence} \\ x=\tan ^{-1}(4) \\ x=75.96 \\ \text{rounded} \\ x=76\text{ \degree} \end{gathered}[/tex]

As 76 is greater than 68, the zipline cable compliance with these regulations.

Also, the hypotenuse (zipline ) is

[tex]\begin{gathered} (MI)^2=(AI)^2+(AM)^2 \\ \text{replace} \\ (MI)^2=(400)^2+(100)^2 \\ (MI)^2=170000 \\ MI=\sqrt[]{17000} \\ MI=412.31\text{ ft} \end{gathered}[/tex]

I hope this helps you

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View image LaneaP454136
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