Answer :
Final answer:
The question can be visualized as a right triangle problem and solved using the tangent function. After including the eye level height in the calculation, the height of the cliff to the nearest foot is approximately 250 feet.
Explanation:
To solve for the height of the cliff, we need to first visualize the problem as a right triangle where our unknown is the height of the cliff. The 186 foot distance from the base of the cliff represents the adjacent side of our triangle, the height of the cliff is our opposite side, and the angle of elevation to the top of the cliff is given as 56°.
First use the tangent function (Tan θ = Opposite/Adjacent), which can be rearranged to solve for the Opposite (height): Opposite = Tan θ * Adjacent We substitute the given values into the equation: Opposite = Tan 56° * 186 feet ≈ 255.3 feet.
However, as the eye level is 5 feet above the ground, we need to subtract this from our calculated height. So, the actual height of the cliff would be 255.3 feet - 5 feet = 250.3 feet.
Therefore, the height of the cliff to the nearest foot is 250 feet.
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