Question

Hi I'm Alina please help me in this math problem

Answer 1

Since theta is the angle between the ladder and the ground

Since the length of the ladder is 16 feet

Since the height of the window from the ground is 12 ft 6 inches

We have to change the inches to feet

Since 1 foot = 12 inches, then

`\begin{gathered} 1feet\rightarrow12inches \\ ?feet\rightarrow6inches \end{gathered}`

By using cross multiplication

`\begin{gathered} ?=(1*6)/(12) \\ ?=(6)/(12) \\ ?=0.5 \end{gathered}`

That means 6 inches = 0.5 feet

The height of the window is 12.5 feet

By using the sine ratio

`sin\theta=(opposite)/(hypotenuse)`

The opposite = 12.5

The hypotenuse = 16

Substitute them in the rule

`\begin{gathered} sin\theta=(12.5)/(16) \\ sin\theta=(25)/(32) \end{gathered}`

By using the inverse of sine

`\begin{gathered} \theta=sin^(-1)((25)/(32)) \\ \\ \theta=51.37516713^(\circ) \end{gathered}`

We can round it to 1 decimal place

`\theta=51.4^(\circ)`

The answer is 51.4 degrees to the nearest one decimal place