Answer:
9
Step-by-step explanation:
This question requires you to use the Pythagorean Theorem. If you're not sure what this is, I'll explain it to you.
The formula itself is: a²+b²=c²
A triangle is composed of two legs and one hypotenuse. The hypotenuse will always be the longest side.
Look at the picture I attached. Here, I helped you label the two legs and the hypotenuse! Now, what do a,b, and c represent in the equation? a will be the first leg, b will be the second leg, and c will be the hypotenuse.
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So, the word problem already gives you two values: the length of the ladder (15') and the height of the wall (12'). If you're having trouble imagining it, look at the second picture I attached where I label the objects with the values they give you. Now we just have to find the missing side.
For the sake of consistency, we're going to call the missing side b. The wall will be a and the ladder will be c. (Go back to the first picture if you're confused.)
Now, we're finally at the part where we plug in our values! All you need to do is put your a and c value into the equation, then solve for b. So:
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12²+b²=15²
(Input 12² and 15² into a calculator unless you've memorized your squares)
Once we square 12 and 15 we get:
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144+b²=225
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Now, the first thing we need to do is get b by itself on one side. So we'll subtract 144 from both sides.
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144+b²=225
-144 -144
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b²=225-144
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b²=81
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Okay, so now we have to get rid of the square over the b. What's the opposite of squaring? (We do the opposite to cancel things on each side, like how we subtracted 144 from each side because it was positive.) That would be finding the square root. So if we do the square root of b, we must do the same thing to the other side:
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√b²=√81
(Type √81 into a calculator unless you've memorized it.)
↓
b=9
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Aaaand... wah-la! We've now found the value of b, or how far from the base of the house we need to be to place a 15' ladder to exactly reach the top of a 12' wall.
I hope you were able to understand my explanation. Please comment if you have any further questions; I will be glad to answer them!
