the base of the ladder is 27.89 ft away from the building
Notice that this situation can be represented with a right angle triangle. The right angle being that made between the ground and the building, the ladder (32 ft long) being the hypotenuse of the triangle, the acute angle of being adjacent to the unknown side we are asked about (x). So, we can use the cosine function to solve this:
which rounded to the nearest hundredth gives;
x = 27.89 ft
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In the picture below, h is height of building and x is the distance the base of the ladder is away from the base of the building.
We use trigonometry to find x, particularly the cosine function.
cos(29.37°) = x/32
cos(29.37°)(32) = x
27.8870633052 = x
We now round off to the nearest hundredths, which means to two decimal places.
27.89 feet = x