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?
Show Work.
First, we need to find the height of the cliff directly in front of you. We can use the tangent function to solve for it:
tan(32°) = opposite / adjacent
tan(32°) = opposite / 1000
opposite = tan(32°) * 1000 ≈ 624.92 ft
Now, we add your eye level height to find the total height:
height of rock climber from the ground ≈ 624.92 ft + 6 ft ≈ 630.92 ft
So, the rock climber is approximately 630.92 ft from the ground.