Question

6.In a 45°- 45°- 90° right triangle, the length of the hypotenuse is 15. How long are the legs?

Answer 1

wait so the other two "legs" are the same right?

Answer 2

your confusing me

Answer 3

sure because two angles are the same

Answer 4

how are you confused?

Answer 5

I dont understand how to get the numbers or anything, i was out the day my teacher taught this and dont get it at all

Answer 6

you have one 90 degree angle, and two 45 degree angles so the legs of the right triangle are equal in length

Answer 7

so when i divide 90 by sqrt 2 i get 45 sqrt 2. what does that mean?

Answer 8

i have confused you, forget what i wrote and lets start again from the beginning

Answer 9

oh ok

Answer 10

is it ok that both legs of the triangle have the same length?

Answer 11

because both angles are the same

Answer 12

yes

Answer 13

ok then lets call them something. lets call them "a"

Answer 14

ok

Answer 15

now lets find the lenght of the hypotenuse using pythagoras

Answer 16

we know pythagoras says \(a^2+b^2=c^2\) for a right triangle yes?

Answer 17

yes

Answer 18

45^2+45^2=90^2

Answer 19

hold on

Answer 20

45 45 90 is not the measure of the lengths of the sides, it is the measure of the angles

Answer 21

pythagoras is about the lengths of the sides, not the message of the angles

Answer 22

oh...then what do we do for this problem?

Answer 23

i am getting to that

Answer 24

s-sorry..

Answer 25

we start with
\[a^2+b^2=c^2\] right? but since the lengths of the legs are both "a" we replace b by a and write
\[a^2+a^2=c^2\] ok?

Answer 26

now we write \(a^2+a^2=2a^2\) so we have \(2a^2=c^2\) and we want to find c

Answer 27

okay so then it would be 45^2 +45^2=90^2 ? right?

Answer 28

take the square root to find the length of c. we get
\[\sqrt{2a^2}=c\]

Answer 29

and we know that
\[\sqrt{a^2}=a\] so what we really have is
\[\sqrt{2}a=c\]

Answer 30

so 4050= 90^2?

Answer 31

in other words, in plane english, if i know the lengths of the sides of a 45-45 -90 right triangle, then i can find the hypotenuse by multiplying by \(\sqrt{2}\)

Answer 32

and if i know the length of the hypotenuse, i can find the length of the sides by dividing by \(\sqrt{2}\)

Answer 33

im still confused.....this isnt helping me very much

Answer 34

please don't square the measures of the angles. it is the lengths of the sides
ok let me say it as simply as i can
your hypotenuse is 15 right? the length of the side is therefore \(\frac{15}{\sqrt{2}}\)

Answer 35

how do i solve the problem........ i understand that is the length of the side....is that the anwser?

Answer 36

yes

Answer 37

if you want a decimal use a calculator and find \(15\div \sqrt{2}\)

Answer 38

but its asking for how long the legs are... not the sides

Answer 39

the legs are the sides

Answer 40

they are synonyms

Answer 41

so all the legs eqaul 15/ sqrt 2

Answer 42

yes

Answer 43

yes, both legs have length \(\frac{15}{\sqrt{2}}\)

Answer 44

if i knew the lenght of the legs was 10, then the length of the hypotenuse would be \(10\sqrt{2}\) and if i know that the length of the hypotenuse is 50 then i know the length of the legs is \(\frac{50}{\sqrt{2}}\)

Answer 45

in other words, so find the hypotenuse multiply by \(\sqrt{2}\) and do find the legs divide the hypotenuse by \(\sqrt{2}\)

Answer 46

By Mr. Pythagoras and his Pythagorean theorem we have
\[a^2+a^2=15^2\]
Where a is the length of the legs
\[2a^2=15^2\]
\[a^2=\frac{15^2}{2}\]
\[a=\sqrt{\frac{15^2}{2}}=\frac{\sqrt{15^2}}{\sqrt{2}}=\frac{15}{\sqrt{2}} \]
I know this is what sat already said. I just thought maybe I would give a go at explaining it since there still seemed to be confusion.