求解MN= m。---**16. Question:** (5 points) As shown in the figure, to measure the mountain height MN, select A and another mountain peak C as observation points. From point A, the angle of elevation of point M, ∠ MAN, is measured to be 60°; the angle of elevation of point C, ∠ CAB, is measured to be 45°; and ∠ MAC is measured to be 75°. From point C, ∠ MCA is measured to be 60°. Given that the mountain height BC is 100m, then the mountain height MN = ____ m. **Chart/Diagram Description:** * **Type:** Three-dimensional geometric figure (perspective drawing). * **Main Elements:** * **Points:** Labeled points are M, N, A, B, C. * **Lines:** * **Solid lines:** MN (vertical), BC (vertical), AM, AC, CM, AB. * **Dashed lines:** AN, NB, NC. These dashed lines appear to define a base plane or connections on a base plane. * **Shapes:** The figure forms a complex 3D structure involving triangles. * Triangle MNA is implied to be a right-angled triangle at N, with MN representing the height and AN being on the ground. * Triangle CBA is implied to be a right-angled triangle at B, with BC representing the height and AB being on the ground. * Triangle MAC is a general triangle in 3D space. * Triangle ANB is a triangle on the implied horizontal ground plane. * **Coordinate Axes:** Not explicitly shown, but verticality of MN and BC implies a z-axis, and A, N, B lie on an implied horizontal (x-y) plane. * **Angles (as given in the text and represented in the diagram):** * ∠MAN = 60° (Angle of elevation from A to M). * ∠CAB = 45° (Angle of elevation from A to C). * ∠MAC = 75°. * ∠MCA = 60°. * **Labels and Annotations:** Points M, N, A, B, C are clearly labeled at their respective vertices. * **Relative Position and Direction:** * MN is a vertical line segment, with M above N. N is on the implied horizontal ground plane. * BC is a vertical line segment, with C above B. B is on the implied horizontal ground plane. * A is an observation point, also on the implied horizontal ground plane. * Lines AM, AC, CM connect the observation point A to the mountain peaks M and C. * Lines AN, AB, NB are connections on the implied horizontal ground plane.