From the edge of a cliff the diagonal distance to the boat is 120 meters. The angle of depression from the edge of the cliff to the boat is 33°. What is the distance between the boat and the base of the cliff?*65.36 meters100.64 meters
Question
From the edge of a cliff the diagonal distance to the boat is 120 meters. The angle of depression from the edge of the cliff to the boat is 33°. What is the distance between the boat and the base of the cliff?*65.36 meters100.64 meters
Solution
To solve this problem, we can use trigonometry. Specifically, we can use the cosine of the angle of depression, which is the adjacent side (the distance from the boat to the base of the cliff) divided by the hypotenuse (the diagonal distance from the edge of the cliff to the boat).
The formula is:
cos(θ) = adjacent / hypotenuse
We know that the hypotenuse is 120 meters and the angle of depression θ is 33°. We want to find the adjacent side (the distance from the boat to the base of the cliff), so we rearrange the formula to solve for the adjacent side:
adjacent = cos(θ) * hypotenuse
Substituting the given values:
adjacent = cos(33°) * 120 meters
Using a calculator to find the cosine of 33 degrees and multiplying by 120, we get approximately 100.64 meters.
So, the distance between the boat and the base of the cliff is approximately 100.64 meters.
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