If you place a 13-foot ladder against the top of a 12-foot building, how many feet will the bottom of the ladder be from the bot
tom of the building?
1 answer:
Answer:
5 feet
Step-by-step explanation:
When you place a 13-food ladder against the top of a 12-foot building, the ladder becomes the hypotenuse of the right angle triangle formed.
Let x be the distance of the bottom of the ladder away from the bottom of the building.
Using the Pythagoras Theorem we obtain:
![{x}^{2} + {12}^{2} = {13}^{2}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7B12%7D%5E%7B2%7D%20%20%3D%20%20%7B13%7D%5E%7B2%7D%20)
This implies that:
![{x}^{2} + 144 = 169](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%20144%20%3D%20169)
![{x}^{2} = 169 - 144](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%20169%20-%20144)
![{x}^{2} = 25](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%2025)
![x = \sqrt{25}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%7B25%7D%20)
![x = 5](https://tex.z-dn.net/?f=x%20%3D%205)
The bottom of the ladder will be 5 feet away from the bottom of the ladder
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