Martha observed a boat from the top of a 74.5 m cliff. She noted that the angle of depression to the boat was 22.70How far is the boat from the base of the cliff ?Round to the nearest 2 decimal places. (Put the numbers only in the box, do not enter any units.)
Question
Martha observed a boat from the top of a 74.5 m cliff. She noted that the angle of depression to the boat was 22.70How far is the boat from the base of the cliff ?Round to the nearest 2 decimal places. (Put the numbers only in the box, do not enter any units.)
Solution
To solve this problem, we can use the tangent of the angle of depression, which is the ratio of the opposite side (height of the cliff) to the adjacent side (distance from the base of the cliff to the boat).
The formula is:
tan(angle) = opposite/adjacent
We know the angle is 22.7 degrees and the opposite side is 74.5 m. We want to find the adjacent side (distance from the boat to the cliff), so we rearrange the formula to solve for the adjacent side:
adjacent = opposite/tan(angle)
Substituting the given values:
adjacent = 74.5/tan(22.7)
Now, calculate the value of tan(22.7) and divide 74.5 by this value.
After calculating, you will get the distance from the boat to the base of the cliff. Remember to round to the nearest 2 decimal places.
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