Question

in one area, the lowest angle of elevation of the sun in winter is 25° 10. find the minimum distance, x, that a plant needing full - sun can be placed from a fence 4.79 ft high.
the minimum distance is □ ft.
(type an integer or a decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle problem where the height of the fence is the opposite side and the distance $x$ is the adjacent side with respect to the given angle of elevation. We use the tangent function $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
The height of the fence (opposite side) $h = 4.79$ ft and the angle of elevation $\theta=25^{\circ}10'$. First, convert $25^{\circ}10'$ to decimal degrees. Since $10'=\frac{10}{60}\approx0.1667^{\circ}$, then $\theta = 25 + 0.1667=25.1667^{\circ}$.

Step2: Set up the tangent equation

We know that $\tan\theta=\frac{h}{x}$, so $x=\frac{h}{\tan\theta}$.
Substitute $h = 4.79$ and $\theta = 25.1667^{\circ}$ into the formula: $x=\frac{4.79}{\tan(25.1667^{\circ})}$.
We know that $\tan(25.1667^{\circ})\approx0.473$.

Step3: Calculate the value of $x$

$x=\frac{4.79}{0.473}\approx10.13$ ft.

Answer:

$10.1$ ft