Question

From a point on the North Rim of the Grand Canyon, the angle of depression to a pointon the South Rim is 2. From an aerial photo, it can be determined that the horizontaldistance between the two points is 10 miles. How many vertical feet is the South Rimbelow the North Rim (nearest whole foot).

Answer 1

Question:

Solution:

The situation of the given problem can be drawn in the following right triangle:

This problem can be solved by applying the trigonometric identities as this:

`\tan(2^(\circ))=(y)/(10)`

solving for y, this is equivalent to:

`y\text{ = 10 tan\lparen2}^(\circ)\text{\rparen=0.349 miles}`

now, 0.349 miles is equivalent to 1842.72 feet. Now, this number rounded to the nearest whole foot is equivalent to 1843.

Then, the correct answer is:

1843 feet.