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Answer:
The height of the pole is 105ft,
Step-by-step explanation:
Let us call the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is
.
The wire length is 14 ft longer than height
, hence
.
Thus we get a right triangle with hypotenuse , perpendicular
, and base
; therefore, the Pythagorean theorem gives
which upon expanding we get:
further simplification gives
,
which is a quadratic equation with solutions
Since the first solution will give the triangle base length of
which is negative; therefore, we disregard it and pick the solution
.
Hence, the height of the pole is 105ft.
The margin of error given the proportion can be found using the formula
Where
is the z-score of the confidence level
is the sample proportion
is the sample size
We have
Plugging these values into the formula, we have:
The result 0.14 as percentage is 14%
Margin error is 38% ⁺/₋ 14%
Where
We have
Plugging these values into the formula, we have:
The result 0.14 as percentage is 14%
Margin error is 38% ⁺/₋ 14%