Can someone help me with this exercise, I am having a difficulty in solving it. It is kinda confusing.

Jim and Jane are walking east toward the main road. Jane decides to cut diagonally to the north at an angle of 30 degrees north of east. Jim continues on for the last 20 feet to the road. How far apart are they when they both reach the road?

The given scenario can be modeled as a right triangle, with Jane's walking path serving as the hypotenuse and Jim's path as the base of the triangle. The distance between Jane and Jim when they reach the road is represented by the side of the triangle opposite the 30° angle, forming the other leg of the triangle. (See attached diagram).

To calculate how far apart Jane and Jim are when they both reach the road, we can use the tangent trigonometric ratio:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Tangent trigonometric ratio}}\\\\\sf \tan(\theta)=\dfrac{O}{A}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{$O$ is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{$A$ is the side adjacent the angle.}\end{array}}[/tex]

Let d be the distance between Jane and Jim.

In this case:

θ = 30°
O = d
A = 20 ft

Substitute the values into the ratio and solve for d:

[tex]\tan30^{\circ}=\dfrac{d}{20}[/tex]

[tex]d=20\tan30^{\circ}[/tex]

[tex]d=11.54700538...[/tex]

[tex]d=11.5\; \sf ft\;(nearest\;tenth)[/tex]

Therefore, the distance between Jane and Jim when they both reach the road is 11.5 ft (rounded to the nearest tenth).