Question

HELP ME UNDERSTAND
If you have a 30-60-90 triangle:

11. And the length of the shortest leg is 4, what's the length of the hypotenuse?

Answer 1

ratios of a 30:60:90 right triangle are \[1:\sqrt3:2\] for
short leg: long leg: hypotenuse

Answer 2

so the hypotenuse is 2?

Answer 3

i can show you why if you like

Answer 4

oh no

Answer 5

yes please I have alot of questions like this

Answer 6

and I need to finish these in like 30 minutes

Answer 7

the hypotenuse is twice the length of the short leg

Answer 8

oh

Answer 9

so if your short leg is 4, then the hypotenuse is ___

Answer 10

8

Answer 11

bingo
next

Answer 12

so next is12. Working from #11, what's the length of the other leg?

Answer 13

the short leg times \(\sqrt3\)

Answer 14

the short leg is times the sqrt of three?

Answer 15

i wouldn't use a calculator, they probably just want you to write \(4\sqrt3\)

Answer 16

lol no dear, the length of the short leg times the square root of three !

Answer 17

Oh okay, is it okay to write it like 4 sqrt 3

Answer 18

yes

Answer 19

13. And the length of the longest leg is 5[SQRT(3)], what's the length of the other leg?

Answer 20

ratios are \[1:\sqrt3:2\] so you have \[4:4\sqrt3:8\]

Answer 21

in this case you have the long leg is \(5\sqrt3\) so the short leg is that number divided by \(\sqrt3\)

Answer 22

in other words, cancel the \(\sqrt3\)

Answer 23

wait so Im confused

Answer 24

just 5?

Answer 25

yes

Answer 26

oh okay

Answer 27

once again ratios are \[1:\sqrt3:2\] you have \[5:5\sqrt3:10\]

Answer 28

14. Working from #13, what's the length of the hypotenuse?

The hypotenuse = 10

Answer 29

is that right

Answer 30

15. And the length of the longest leg is 9, what is the length of shortest leg?

Answer 31

yes to 14

Answer 32

for 15 the short leg is half of the hypotenuse

Answer 33

oh oops scratch that

Answer 34

the long let is 9, the short let is 9 divided by the square root of three
lets be careful how to compute that

Answer 35

would we just do 9/ sqrt 3 ?

Answer 36

\[\frac{9}{\sqrt3}\] is one answer, but they probably want you to do this \[\frac{9}{\sqrt3}\times \frac{\sqrt3}{\sqrt3}=\frac{9\sqrt3}{3}=3\sqrt3\]

Answer 37

oh okay

Answer 38

the last one \(3\sqrt3\) is the same number, just in "simplest radical form"

Answer 39

16. Working from #15, what is the length of the hypotenuse?

Answer 40

double the short leg

Answer 41

so it would be double the shortest leg

Answer 42

you are getting it i see

Answer 43

but the shortest leg is 3 sqrt 3

Answer 44

right
multiply that by 2

Answer 45

6 sqrt 6

Answer 46

oh no just \(6\sqrt3\) not \(6\sqrt6\)

Answer 47

oh okay

Answer 48

on account of \[2\times 3\sqrt3=6\sqrt3\] just like \[2\times 3x=6x\]

Answer 49

17. With a hypotenuse of 2[SQRT(3)] what is the length of the longest leg?

Answer 50

ohhh and i see

Answer 51

the short leg is ...

Answer 52

the answer is 2

Answer 53

nope

Answer 54

dang

Answer 55

divide the hypotenuse by 2 to get the short leg
the long leg is 2

Answer 56

wait wait

Answer 57

ok

Answer 58

so 2/2 is 1

Answer 59

right is that what im doing?

Answer 60

this one confuses me

Answer 61

right
lets back up a second cause i made a mistake

Answer 62

the hypotenuse is \(2\sqrt3\) right?

Answer 63

yes

Answer 64

the short leg is therefore half of that

Answer 65

so the sqrt 3 cancels out right?

Answer 66

no not dividing by \(\sqrt3\)
just divide by 2

Answer 67

oh so 1

Answer 68

\[\frac{2\sqrt3}{2}=?\]

Answer 69

think of it like \[\frac{2x}{2}\]

Answer 70

im still really confused

Answer 71

ok i don't want to confuse you lets see if i can explain
the short leg is half the hypotenuse
whatever the hypotenuse is, divide it by 2
half of \(2\sqrt3\) is \(\sqrt3\)

Answer 72

just like half of \(2x\) is \(x\)

Answer 73

Ohhhhokay

Answer 74

so the short leg is just sqrt 3

Answer 75

yes, exactly

Answer 76

now i bet you need the long leg right?

Answer 77

right

Answer 78

it is the short leg times \(\sqrt3\)
since the short leg is \(\sqrt3\) itself, you need to multiply \[\sqrt3\times \sqrt3\]

Answer 79

sqrt 9

Answer 80

I think

Answer 81

lol yeah but c'mon what is
\(\sqrt9\)?

Answer 82

3