The top of a ladder rests at a height of 15 feet against the side of a house. If the base of the ladder is 6 feet from the house
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Answer:
25.61 feet
Step-by-step explanation:
First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.
Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.
One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have
sin(80°) = opposite / 26 feet
multiply both sides by 26 feet
sin(80°) * 26 feet = opposite
= 25.61 feet as the height of the wall the ladder reaches
