Question

Geometry: How does the length of the hypotenuse in a right triangle relate to the lengths of the legs?

Answer 1

Via the pythagoran theorem

\[\large a^2 + b^2 = c^2\]

c is the hypotenuse of the right triangle
and a and b are the legs

Answer 2

Look up Pythagoras' Theorem and see if you can tell me the answer.

Answer 3

Can you help me with one more? @johnweldon1993

Answer 4

There are many people who can so if I cannot then I'm sure someone else will :)

Answer 5

Okay.
How do you find the value of x? What is it?

Answer 6

We have 2 legs known...and 1 angle...if we use the law of cosines to solve for side c...and then the law of sines to solve for the missing angle

\[\large c^2 = a^2 + b^2 - 2ab(cos(c))\]

Doing that...we can now see that we have 3 sides...and we set up the law of sines

\[\large \frac{sin(a)}{A} = \frac{sin(b)}{B} = \frac{sin(c)}{C}\]

So we plug in whatever sides we know..and solve for the angle 'x'

\[\large \frac{sin(38)}{\text{side c we just solved for with the law of cosines}}=\frac{sin(x)}{21}\] and solve for 'x'

Answer 7

don't work so hard...this is an isosceles triangle

Answer 8

Yeah I just noticed that XD, this method will still work however @ayyookyndall

Answer 9

Okay. So what sin(x)? Im still kinda confused.

Answer 10

Is there an easier way to find out?

Answer 11

Yeah true, probably nothing you've seen before

Lets look at it the easier way

Answer 12

(one leg)^2 + (the other leg)^2 = (hypotenuse)^2

Answer 13

so since we know those 2 angles are equal...and the sum of all the angles in the triangle add to 180...we can solve for 'x'

Answer 14

Okay so the x are 21. Do I add it up with 38?

Answer 15

Noooo no I merely put 'x' to show that those 2 sides are equal...nothing to do with the angles...sorry

So we have the angle we know..which is 38....and we know that the other 2 angles are the same

so if that angle is called 'a' we would have 2a

So if we add

2a + 38

we know that has to = 180...so

\[\large 2a + 38 = 180\]

and solve for 'x' *which will be your 'x' in your question

Answer 16

ugh, solve for 'a' sorry for the typo

Answer 17

Wow, I feel so dumb.
Whats the formula to help solve for this?

Answer 18

Oh the answer is 70.
But is there a formula that goes with this? @johnweldon1993

Answer 19

70 is not correct

Answer 20

Really? Are you sure? @Zarkon

Answer 21

you are very close

Answer 22

If a triangle adds up to 180

180-38= 142
142/2 = 70

Answer 23

142/2=71

Answer 24

Oh. Gosh. Now I feel dumber.
Anyways is there a formula to go with this?

Answer 25

just the equation you used