Question

Avalanche conditions: Winter avalanches occur for many reasons, one being the slope of the mountain. Avalanches seem to occur most often for slopes between 35° and 60° (snow gradually slides off steeper slopes). The slopes at a local ski resort have an average rise of 2000 ft for each horizontal run of 2559 ft. Is this resort prone to avalanches? Find the angle θ and respond. 2000 ft 2559 ft

Answer 1

Yes, since angle θ = 38° and is between 35° and 60°, this slope is prone to avalanches.

Explanation:

Avalanche conditions: Winter avalanches occur for many reasons, one being the slope of the mountain. Avalanches seem to occur most often for slopes between (snow gradually slides off steeper slopes). The slopes at a local ski resort have an average rise of 2000 ft for each horizontal run of 2559 ft. Is this resort prone to avalanches? Find the angle θ and respond. 2000 ft 2559 ft

Draw a right triangle. Start with a horizontal side and label the horizontal side 2559 ft. Then at one endpoint of that side, draw a vertical side going up from the horizontal side. Label it 2000 ft. Connect the upper point of the vertical side to the other endpoint of the triangle. The acute angle at the bottom is θ.

`\tan \theta = (opp)/(adj)`

`\tan \theta = (2000)/(2559)`

`\theta = \tan^(-1) 0.7816`

`\theta = 38^\circ`

Since the angle is between 35° and 60°, this slope is prone to avalanches.