It doesn't sound right when you have a 15 ft. ladder leaning against a wall with the foot of the ladder 36.9 ft away.
So you need to recheck your work when it does not look right.
The length of the ladder is the hypotenuse of the right triangle.
The base of the ladder is adjacent to the 66° angle, so by definition of cosine,
Distance from the wall
= hypotenuse * cos(66°)
= 15 cos(66°)
= 6.1 ft approximately.
A 15 ft. ladder is leaning against the side of a house and forms an angle of 66o with the ground. To the nearest foot how far from the base house is the foot of the ladder?
I set it up cos66=15/x
15/cos66 =36.878, rounding to the nearest ft makes it 37
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