To measure a stone face carved on the side of a mountain, two sightings 900 feet from the base of the mountain are taken. If the angle of elevation to the bottom of the face is ${25}^{\circ }$ and the angle of elevation to the top is ${28}^{\circ }$, what is the height of the stone face?
The height of the stone face is $◻$ feet.
(Do not round until the final answer. Then round to two decimal places as needed.)

Step 1 ：Let's denote the height from the ground to the bottom of the face as $h1$ and the height from the ground to the top of the face as $h2$.

Step 2 ：We can set up two equations, one for the bottom of the face and one for the top, using the tangent of the angles of elevation. The tangent of an angle in a right triangle is equal to the opposite side (the height we're trying to find) divided by the adjacent side (the distance from the base of the mountain, which is 900 feet).

Step 3 ：So we have: $\tan (25)=\frac{h1}{900}$ and $\tan (28)=\frac{h2}{900}$

Step 4 ：Solving these equations for $h1$ and $h2$, we get $h1=900\times \tan (25)$ and $h2=900\times \tan (28)$

Step 5 ：Subtracting $h1$ from $h2$ gives us the height of the face: $h2-h1$

Step 6 ：Substituting the values we found for $h1$ and $h2$, we get $900\times \tan (28)-900\times \tan (25)$

Step 7 ：Calculating this gives us the height of the stone face.

Step 8 ：Final Answer: The height of the stone face is $\boxed{{\displaystyle 58.86}}$ feet.