Question

I have to find the range of the height of a pine tree. its standing up beside a right triangle. The shadow of the tree is 8 ft. The hypotenuse is 17 ft. How would I do this to figure out my answer?

Answer 1

Pythagorean theorem

a²+b²=c²

Answer 2

\( \large 8^{2} + x^{2}=17^{2}\)

Answer 3

So how would I find the range of the pine tree?

Answer 4

if you find the value of x, you'll know the height of the tree

Answer 5

So i fid x by subtracting 8 from both sides?

Answer 6

that would be a good start

Answer 7

okay so I did 8^2-8^2 which is 0. so that cancels out so al i have left is x^2=225. because I did 17^2-8^2

Answer 8

correct

Answer 9

so if \[\large x^{2}=225 \] then x=?

Answer 10

x=225?

Answer 11

if you go from x² to x, you do \[\large \sqrt{x²} = x\]

Answer 12

so if you take the root of one side of the = sign, you have to do it on the other side as well

Answer 13

x=15

Answer 14

correct

Answer 15

So how would I find the range of the height of the triangle. I have to do the triangle inequality theorem.

Answer 16

Eh, i don't understand the question

Answer 17

It says find the range of the pine tree by using the triangle inequality theorem.

Answer 18

I think i misinterpret the question then, hold on.

Answer 19

yes but that's not really the triangle inequality theorem, i never used that before either.

Answer 20

Well, it says to find the range of the pine tree. but i can refer to the triangle inequality theroem.

Answer 21

Ok, so i googled a around a bit and apperantly x+8>18 so the tree can't be smaller then 10, but we don't know the upper limit yet then... http://www.mathopenref.com/triangleinequality.html

Answer 22

Okay thanks.

Answer 23

oh wait it;'s obvious actually

Answer 24

it can never be longer then 18+8 either i guess, so it's between 10 and 26 i guess

Answer 25

at least f i understood the theorem correctly.

Answer 26

Thats good. It really helped me.
I need to find all 3 triginometric ratios using angle a.