Question

a 18ft ladder is leaning against a wall. the wall is 16.5 feet tall. find the length from the foot of the ladder to the wall. show work

Answer 1

@Juila12001 How do you think we solve for that last side?

The hypotenuse is the ladder, the right leg is the wall, and the bottom leg is the distance from the foot ladder to the wall.

Answer 2

you divide the numbers?

Answer 3

Well, have you heard of Pythagorean's Theorem?

Answer 4

yea a^2 +b^2+c^2

Answer 5

Yes! It only works with right triangles, and this ladder creates a right triangle with the wall and the floor. Do you know how to use the formula?

Answer 6

no

Answer 7

As you said, the formula is:

\[a^2 + b^2 = c^{2}\]

'a' and 'b' are the legs, whilst 'c' is the hypotenuse.

Answer 8

Earlier we identified some of the sides of the triangle. They gave us two measurements, and earlier what sides they correspond to. Do you remember what they are?

Answer 9

Trust me that this problem is very simple. If you are confused with anything, just let me know.

Answer 10

18 AND 16.5

Answer 11

18 is what side?

Answer 12

leg or hypotenuse

Answer 13

Hypotenuse

Answer 14

Correct. There is only one hypotenuse, so that means that 16.5 is a leg.

'c' is the hypotenuse
'a' and 'b' are legs

\[a^2 + b^2 = c^{2}\]

Input Variables
\[(16.5)^2 + b^2 = (18)^2\]
Do Exponents
\[272.25 + b^2 = 324\]
Isolate b^2 by subtracting 272.25
\[b^2 = 51.75\]
Isolate b by taking the square root of both sides since sqrt (b^2) = b
\[b = 7.19374728497\]

Answer 15

Usually teachers want you to round such numbers, so b = 7.2 (rounded to the tenth place)

Answer 16

thank you

Answer 17

No problem. Let me know if you have any more questions.