We can use trigonometry to solve this problem.
Let h be the height of the rock climber from the ground.
From the information given, we can draw a right triangle as follows:
- The horizontal distance from your eye level to the base of the cliff is 1000 ft.
- The angle of elevation from your eye level to the top of the cliff (where the rock climber is) is 32°.
- Your eye level is 6 ft. above the ground.
We can use the tangent function to find h:
tan(32°) = h / (1000 ft + 6 ft)
Simplifying and solving for h, we get:
h ≈ (1000 ft + 6 ft) * tan(32°)
h ≈ 579.5 ft
Therefore, the approximate height of the rock climber from the ground is 579.5 ft.
You sight a rock climber on a cliff at a 32° angle of elevation. Your eye level is 6ft. above the ground and you are 1000ft. from the base of cliff. What is the approximate height of the rock climber from the ground?
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