Final answer:
To find the angle of ascent of a branch trail from a steep route, use trigonometry and the concept of right triangles. Subtract the slope angle of the route from the angle at which the branch trail intersects the route.
Step-by-step explanation:
When climbing a mountain up a steep route with a certain slope angle, if you come upon a trail branching off at a different angle, you can find the angle of ascent of the branch trail using trigonometry.
To do this, you can use the concept of right triangles and the tangent function. The slope angle of your route represents the angle between the uphill direction and the horizontal, let's call it angle A. The angle of ascent of the branch trail can be found by subtracting angle A from the angle at which the branch trail intersects your route, let's call it angle B. So, the angle of ascent of the branch trail is given by the equation: angle of ascent = angle B - angle A.
For example, if your route has a slope angle of 30° and the branch trail intersects your route at a 45° angle, the angle of ascent of the branch trail would be 45° - 30° = 15°.