Answer: About 15 feet off the ground
The more accurate value is 14.6167273222817 but even this value is not fully exact.
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Work Shown:
Refer to the diagram below.
sin(angle) = opposite/hypotenuse
sin(66) = x/16
16*sin(66) = x
x = 16*sin(66)
x = 14.6167273222817
x = 15
The ladder reaches roughly 15 feet off the ground, when rounding to the nearest whole number.
I'm rounding to the nearest whole number since the other length (16 ft) is a whole number. Round however you need to if your teacher instructs otherwise.