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 \(\boxed{58.86}\) feet.