Question

How to solve these.Also how to do number 8 in miles .

Answer 1

The maximum height on the top of the slide is 0.001947 mile

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

`\begin{gathered} \sin \text{ }\theta\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \text{ where }\theta=40^o \\ \sin \text{ 40 = }(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}`

Hence, the maximum height on the top of the slide is 10.28ft

The next thing is to convert ft to mile

`\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}`

Hence, 10.28ft is 0.001947 mile