Question

At the Grand Canyon, a hiker is looking in awe at the base of another cliff with an angle of depression from 52 degrees. Knowing that they are a horizontal distance of 2000 feet from where they stand to where the top of the Cliff is, how high up is the other cliff to the nearest foot?

Answer 1

6,445 feet

Explanation:

90-52 = 38

x =
`(2000)/(tan 38)`

x = 6445

Answer 2

• 2560 feet

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Let the height of the other cliff be h.

The angle opposite to h is 52 degrees and the horizontal distance is 2000 feet. The two lengths are the legs of a right triangle.

Use tangent to find the value of h:

• tangent = opposite leg / adjacent leg
• tan 52° = h / 2000
• h = 2000 tan 52°
• h = 2560 feet (rounded to the nearest foot)