Question

Can someone help me with number 31 in the image below?

Answer 1

are you getting the image?

Answer 2

Oops, it showed it attached when i uploaded the question

Answer 3

Here's the problem

Answer 4

Well, we know that the total height is 18ft

That 18 ft is now split between the hypotenuse of the triangle and what is left standing

Answer 5

3, 4,5 and 5, 12, 13 should be memorized

Answer 6

now you can just see the right triangle and has one side of 12, and go " oh, I recognize 5, 12, 13 as sides of right triangles!

Answer 7

since 12, is one of the side, and 5+13 is 18, you are be sure you are correct, this is probably the fastest way to do this problem

Answer 8

^True that is a quick way to do this, Pythagorean triplets are a good thing to have in the back pocket...if you weren't that lucky.it would follow this process:

We can say that \(\large x + h = 18\)

so solving that for 'x' we find that \(\large x = 18 - h\)

So now we just use the Pythagorean identity of \(\large a^2 + b^2 = c^2\)

Or in this case \(\large 12^2 + h^2 = (18 - h)^2\)

Lets simplify

\[\large 144 + h^2 = 324 - 36h + h^2\]

Notice

\[\large 144 + \cancel{h^2} = 324 - 36h + \cancel{h^2}\]

So what we have is

\[\large 144 = 324 - 36h\]

Or \(\large h = \frac{144 - 324}{-36} = 5\)