i feel like this answer is wrong...please help!

[lea]

There is a bamboo 20 ft high in which the upper end breaks and falls to the ground 6 ft from the stem. Set up and solve an equation that can be used to find the exact height of the break and exactly how much broke off.

I used a^2+b^2=c^2

I drew a right triangle and labeled the base (b) as 6 ft and side (a) as the height 20ft

c^2=6^2+20^2
c^2=36+400

The square root of c^2 = the square root of 436
C= 20.88

Than because the bamboo is 20 ft high I would subtract 20.88-20.00= .88 would be how much broke off?

 

[Deleted member 4993]

There is a bamboo 20 ft high in which the upper end breaks and falls to the ground 6 ft from the stem. Set up and solve an equation that can be used to find the exact height of the break and exactly how much broke off.

I used a^2+b^2=c^2

I drew a right triangle and labeled the base (b) as 6 ft and side (a) as the height 20ft

c^2=6^2+20^2
c^2=36+400

The square root of c^2 = the square root of 436
C= 20.88

Than because the bamboo is 20 ft high I would subtract 20.88-20.00= .88 would be how much broke off?

Assume that the bamboo broke off at a height of h.

Then the fallen part is (20-h) and it makes the hypotenuse for the broken bamboo. We have:

h2 + 6^2 = (20-h)^2

solve for h from above.

 

[lea]

my work

h^2+6^2=20^2+h^2
h^2+6^2=(20-h)*(20-h)
h^2+36=400+h^2
-36 -36
h^2=364+h^2
-h^2=364-h^2
square root of 364=19.08

20.00-19.08=.92 break ??

 

[Mrspi]

h^2+6^2=20^2+h^2
h^2+6^2=(20-h)*(20-h)
h^2+36=400+h^2
-36 -36
h^2=364+h^2
-h^2=364-h^2
square root of 364=19.08

20.00-19.08=.92 break ??

You have an error. (20 - h)*(20 - h) is NOT 400 + h^2

(20 - h)*(20 - h) = (20 - h)* 20 + (20 - h)*(-h)
or,
20*20 - h*20 + 20*(-h) - h*(-h)
or
400 - 20h - 20h + h^2
Or.....

400 - 40h + h^2

Substitute that into your equation (line 3) and you'll have

h^2 + 36 = 400 - 40h + h^2

Continue......

 

[lea]

Maybe this time?

h^2+36=400-40h+h^2
-h^2 -h^2
36=400-40h

bring the -40h to the left

40h+36=400
-36 -36
40h=364 divide both sides by 40
h=9.1

20.00-9.1=10.90

So 9.1 ft is the amount that broke off
10.90 ft is the height of the break ?