ANSWER
The maximum height on the top of the slide is 0.001947 mile
STEP-BY-STEP EXPLANATION:
Given parameters
• Angle of elevation = 40 degrees
,
• The length of the slide = 16 ft
The next thing is to interpret this using a diagram
Let the maximum height on the top of the slide be x
To solve for x, we will be using the SOH CAH TOA rule
From the above diagram
• The hypotenuse side = 16 ft
,
• The opposite side = x ft
The next thing is to find x using the SOH rule
[tex]\begin{gathered} \sin \text{ }\theta\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \text{ where }\theta=40^o \\ \sin \text{ 40 = }\frac{x}{16} \\ \text{Cross multiply} \\ x\text{ = 16 }\cdot\text{ sin 40} \\ \sin \text{ 40 = 0.6428} \\ x\text{ = 16 }\cdot\text{ 0.6428} \\ x\text{ = }10.28\text{ ft} \end{gathered}[/tex]
Hence, the maximum height on the top of the slide is 10.28ft
The next thing is to convert ft to mile
[tex]\begin{gathered} 1ft\text{ = 0.000189394 mile} \\ 10.28ft\text{ = x mile} \\ \text{cross multiply} \\ 1\cdot\text{ x = 0.000189394 }\cdot\text{ 10.28} \\ x\text{ = }0.001947\text{ mile} \end{gathered}[/tex]
Hence, 10.28ft is 0.001947 mile
