Question

Driving down a​ mountain, Bob Dean finds that he descends 6000 feet in elevation by the time he is 4.5 miles​ (horizontally) away from the high point on the mountain road. Find the slope of his descent.​ (1 mile​ = 5280​ feet).

Answer 1

Answer:

Slope of descent is 14.17°

Step-by-step explanation:

As given in the question Bob Dean finds that when he descends height AB = 6000 feet, by the time he is 4.5 miles (BC) away from the high point on the mountain road.

We have to find the slope (measure of ∠C) as given in the figure attached.

First we will convert length of BC = 4.5 miles into feet to make all units uniform.

∵ 1 mile = 5280 feet

∴ 4.5 miles = 5280×4.5 feet

                  = 23760 feet

Since angle of descent is always equal to the angle of elevation

So slope = tanC = $\frac{AB}{BC}$

                              = $\frac{6000}{23760}$

                              = 0.2525

C = $tan^{-1}(0.2525)$

  = 14.17°

Therefore, slope of his descent is 14.17°.