A 26-foot ladder leaning against the side of a house makes a 60∘60∘ angle with the ground. How far up the side of the house does the ladder reach?
Question
A 26-foot ladder leaning against the side of a house makes a 60∘60∘ angle with the ground. How far up the side of the house does the ladder reach?
Solution
Sure, I can help with that. This is a trigonometry problem. We can use the sine of the angle to find the height that the ladder reaches up the side of the house. The sine of an angle in a right triangle is defined as the length of the opposite side (the height the ladder reaches up the house) divided by the length of the hypotenuse (the length of the ladder).
So, we can set up the equation as follows:
sin(60) = height / 26
To solve for height, we multiply both sides by 26:
height = 26 * sin(60)
Using a calculator, we find that sin(60) is approximately 0.866. So:
height = 26 * 0.866
Therefore, the ladder reaches approximately 22.5 feet up the side of the house.
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