Question

does anyone know how to solve special right triangles?

Answer 1

??? https://calcworkshop.com/triangle-trig/special-right-triangles/

Answer 2

Did you already get help?

Answer 3

no i didnt

Answer 4

Okay I can help-

Answer 5

i just need an explanation on how to do it, thank you!

Answer 6

Okie dokie... so do you know the Pythagorean Theorem ?

Answer 7

um just a little not alot

Answer 8

Well the Pythagorean Theorem is a^2+b^2=c^2.

Answer 9

Do you know what a hypotenuse is ?

Answer 10

yes i do

Answer 11

Ok, well the c^2 part is the hypotenuse in the equation. Lemme draw you something rq.

Answer 12

okay

Answer 13

so... that big side is the c^2.

Answer 14

ok got it

Answer 15

how would you go about finding the missing sides of the triangle?

Answer 16

Ok, well I just went on a whole different route... Ignore all that. Ok here's what you really need to know. Lemme draw another thing rq.

Answer 17

this is the equation we're going to start with.

Answer 18

okay

Answer 19

Ok to start off... we need to identify all the angles of the triangle.

Answer 20

Can you tell me what the angles are?

Answer 21

45,45,90

Answer 22

Okay... well there is different rules for (45.45.90) and (30,60,90) triangles.

Answer 23

In a 45,45,90... the legs (the other sides other than the hypotenuse) are found by dividing the hypotenuse by \[\sqrt{2}\]

Answer 24

To find the hypotenuse, you multiply the legs by \[\sqrt{2}\]

Answer 25

You find the "long side" by multiplying the side by the square root of 2.

Answer 26

but where did the 1 come from

Answer 27

\(\color{#0cbb34}{\text{Originally Posted by}}\) @nikkixmarie
but where did the 1 come from
\(\color{#0cbb34}{\text{End of Quote}}\)
The 1 is the measure of the side, not the hypotenuse.

Answer 28

why are these triangles special right triangles ?

Answer 29

Don't think too hard... the 1 is just the measure of the side, that's all.

Answer 30

oh okay

Answer 31

just use the law of sin or cos and solve them

but you need to know the trigonometrical value of sin 45° or cos 45° and so much

Answer 32

4?

Answer 33

\(\color{#0cbb34}{\text{Originally Posted by}}\) @nikkixmarie
4?
\(\color{#0cbb34}{\text{End of Quote}}\)
Correct~

Answer 34

So now you have the answer to your first question.

Answer 35

Wait wait wait-

Answer 36

We still need to find B- but in a 45, 45, 90 triangle... the 2 sides are the same, EXCEPT for the hypotenuse.

Answer 37

okay, these are so hard there is still 4 more after this ill try to figure them out

Answer 38

Do you want me to go slower ? What can I do to help ?

Answer 39

no its fine its just confusing to me thats all

Answer 40

Ok... well we're gonna try the 2nd one, lemme draw it rq-

Answer 41

what are the angles in the triangle ?

Answer 42

45,45,90

Answer 43

Special right triangles follow the form 45, 45, 90
or 30, 60, 90
These are angle measures and their corresponding side lengths are
\[x, x, \sqrt{x}\]
and \[x, x \sqrt(3), 2x\]
respectively

Answer 44

For example if you are given a 45-45-90 triangle, and they say the length of a side opposite one of the 45 degree angles is 5, the side opposite the other 45 degree angle is also 5 and the hypotenuse is \[5\sqrt{2}\]

Answer 45

the legs are missing btw

Answer 46

\(\color{#0cbb34}{\text{Originally Posted by}}\) @nikkixmarie
the legs are missing btw
\(\color{#0cbb34}{\text{End of Quote}}\)
Ok remember how I said that the legs are equal in a 45, 45, 90 ? Well, that means x and y are equal, so let's solve for the legs...

Answer 47

in that case other way around. If you know hypotenuse in a 45-45-90 triangle the legs are equal to the hypotenuse divided by sqrt(2)

Answer 48

so when you divide the hypotenuse by that you are given the legs?

Answer 49

so my opinion that all what you need to know

- the law of sin and cos

and that

sin45° = cos45° = \[\frac{ \sqrt{2} }{ 2 }\]

Answer 50

for a 45-45-90 degree yes @nevaehhh

Answer 51

correct @jhonyy9 think about how the 45-45-90 is defined on a unit circle. You take the sin(45) which is the opposite/hypo
then sin(45) = x/1
so x = sin(45) = sqrt(2)/2

Answer 52

if yall could let me have this one- you see im only 47👉🏼👈🏼

Answer 53

thats the case for the hypo being 1
if the side was 1 then we divide the hypo by sqrt(2)/2 or multiply by 2/(sqrt(2))
to get us the value

Answer 54

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
Special right triangles follow the form 45, 45, 90
or 30, 60, 90
These are angle measures and their corresponding side lengths are
\[x, x, \sqrt{x}\]
and \[x, x \sqrt(3), 2x\]
respectively
\(\color{#0cbb34}{\text{End of Quote}}\)
which is where this comes in

Answer 55

I feel bad for not understanding still, im confused again

Answer 56

\(\color{#0cbb34}{\text{Originally Posted by}}\) @nikkixmarie
I feel bad for not understanding still, im confused again
\(\color{#0cbb34}{\text{End of Quote}}\)
what are you confused about ?

Answer 57

@nevaehhh feel free to help out. \(\color{#0cbb34}{\text{Originally Posted by}}\) darkknight
\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
Special right triangles follow the form 45, 45, 90
or 30, 60, 90
These are angle measures and their corresponding side lengths are
\[x, x, \sqrt{x}\]
and \[x, x \sqrt(3), 2x\]
respectively
\(\color{#0cbb34}{\text{End of Quote}}\)
which is where this comes in
\(\color{#0cbb34}{\text{End of Quote}}\)
use this for it

Answer 58

Just solve the equation I gave you... look at the drawing rq.

Answer 59

is it 2

Answer 60

\(\color{#0cbb34}{\text{Originally Posted by}}\) @nikkixmarie
is it 2
\(\color{#0cbb34}{\text{End of Quote}}\)
Around 2.83 to be exact

Answer 61

But... what does this mean ? What do x and y equal ?

Answer 62

the 2.83

Answer 63

\(\color{#0cbb34}{\text{Originally Posted by}}\) @nikkixmarie
the 2.83
\(\color{#0cbb34}{\text{End of Quote}}\)
good job- x=2.83 and y=2.83

Answer 64

Do you want me to do the next question with you ?

Answer 65

can i try to solve it then you tell me if its right?

Answer 66

Absolutely.

Answer 67

yea i need help with this one the hypotenuse is confusing

Answer 68

i mean the leg sorry

Answer 69

You were right the first time, we're solving for the hypotenuse-

Answer 70

wait what do you multiply again the find the hypotenuse.

Answer 71

to*

Answer 72

so 3?

Answer 73

Yep- that's right

Answer 74

3 would be the hypotenuse and the other equation would be the leg

Answer 75

Yep- the other leg would equal the other one lmao-

Answer 76

ohhhhhh

Answer 77

But the hypotenuse is 3.

Answer 78

ok i got it noww

Answer 79

Okie dokie~ hope i helped lmao

Answer 80

you did so much thank you!

Answer 81

\(\color{#0cbb34}{\text{Originally Posted by}}\) @nikkixmarie
you did so much thank you!
\(\color{#0cbb34}{\text{End of Quote}}\)
you're welcome :)

Answer 82

u need to be promoted girl

Answer 83

\(\color{#0cbb34}{\text{Originally Posted by}}\) @nikkixmarie
u need to be promoted girl
\(\color{#0cbb34}{\text{End of Quote}}\)
PREACHHH- i really do smh😭

Answer 84

yessss fr omg