Question

A plane hillside is inclined at an angle of 28° with the horizontal. A man wearing skis can climb this hillside by following a straight path inclined at an angle of 12° to the horizontal, but one without skis must follow a path inclined at an angle of only 5º with the horizontal. Find the angle between the directions of the two paths. a. . 15-56° b. 13.21° c. 18.74° d. 17.22°

Answer 1

The angle between the directions of the two paths is 17°.

Step-by-step explanation:

To find the angle between the directions of the two paths, we need to consider the components of the paths that are perpendicular to the hillside. The path for the man wearing skis has an angle of 12° with the horizontal and an angle of 40° (90° - 50°) with the hillside. The path for the man without skis has an angle of 5° with the horizontal and an angle of 23° (90° - 67°) with the hillside.

Therefore, the angle between the directions of the two paths can be found by subtracting the two hillside angles: 40° - 23° = 17°