Question

3. Solve the problem.In one area, the lowest angle of elevation of the sun in winter is 24°. Find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high. Round your answer to the tenthsplace when necessary.

Answer 1

The breakdown of the image of the question is given below as

Concept:

To figure out the value of x, we will use the trigonometric ratio below

`\begin{gathered} \tan\theta=(opposite)/(adjacent) \\ opposite=10.5ft \\ adjacent=x \\ \theta=24^0 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \tan\theta=(oppos\imaginaryI te)/(adjacent) \\ \tan24^0=(10.5ft)/(x) \\ \end{gathered}`

By cross multiplying the equation above, we will have

`\begin{gathered} \tan24^0=(10.5ft)/(x) \\ x*\tan24^0=10.5ft \\ divide\text{ both sides by tan24} \\ (x*\tan24^0)/(tan24^0)=(10.5ft)/(\tan24^0) \\ x=23.58ft \\ x\approx23.6ft(nearest\text{ tenth\rparen} \end{gathered}`

Hence,

The final answer is

`\Rightarrow x=23.6ft`