Chapter 4.8, Problem 19E

Solution

To find: The width of the canyon at that point.

The width of the canyon at that point is approximately 3133.64 ft.

Given information:

Given, the angle of depression is 19° from a point 7256 ft above sea level on the north rim of the Grand Canyon to a point 6159 ft above sea level on the south rim.

Calculation:

The height of the north rim above the south rim is 7256-6159=1079 ft

Since the angle of depression from the top of north rim is 19°, the angle from the top of south rim to north rim is also 19° (Since alternate angles)

The figure representing the data is:

  

Using definitions of trigonometric functions for the triangle ABC:

  $\begin{array}{c}\tan \left(CBA\right)=\frac{\text{opposite side}}{\text{adjacent side}}\\ \tan \left(19°\right)=\frac{1079}{w}\\ w=\frac{1079}{0.344}\\ w\approx 3133.64\end{array}$

The width of the canyon at that point is approximately 3133.64 ft.

Conclusion:

The width of the canyon at that point is approximately 3133.64 ft.