14. At a certain distance from the base of a tree a student surveyor measures the angle of elevation to be 44 degrees to the top of a tree. Then the surveyor moves farther away from this point by a distance of $70 \mathrm{~m}$. The angle of elevation again to the top of the tree is measured by the surveyor to be 25 degrees. How tall is the tree rounded to the tenth of a metre? Draw a diagram.

Step 1 ：Let the height of the tree be h, the initial distance from the base of the tree be x, and the angle of elevation at the first point be A (44 degrees) and at the second point be B (25 degrees).

Step 2 ：Set up two equations using the tangent function: \(\tan(A) = \frac{h}{x}\) and \(\tan(B) = \frac{h}{x+70}\).

Step 3 ：Solve these equations simultaneously to find the height of the tree (h).

Step 4 ：Calculate the tangent of A and B: \(\tan(44) \approx 0.9657\) and \(\tan(25) \approx 0.4663\).

Step 5 ：Substitute the tangent values into the equations: \(0.9657 = \frac{h}{x}\) and \(0.4663 = \frac{h}{x+70}\).

Step 6 ：Solve the equations to find x and h: x ≈ 63.12 and h ≈ 60.96.

Step 7 ：Round the height of the tree to the nearest tenth: \(\boxed{61.0}\) meters.