Question

find the interior angles of the triangle whose sides are 12cm,15cm,22cm. WITH MEDAL

Answer 1

Do you know how to start?

Answer 2

no

Answer 3

Have you heard of the Cosine Rule?

Answer 4

no

Answer 5

It's sort of similar to the Pythagorean theorem but it works for all triangles.

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

Answer 6

So just plug those numbers into your calculator and solve.

Answer 7

wait so the answer is

Answer 8

its veryv hard :(

Answer 9

It's ok, you can do it...

Answer 10

teach me step by step

Answer 11

Did you try plugging in those numbers into the formula I gave you?

Answer 12

yes
12^2=15^2+22^2-2(15)(22) cos

Answer 13

ok, now multiply those out

Answer 14

144=225+484-660 cos

Answer 15

144 = 225 + 484 - 660 cos(A)

Now, simplify the expression so that you have "cos(A)" on one side and everything else on the other side.

Answer 16

144=49cosA?

Answer 17

No, more like this:

\[\frac{ 144 -225 - 484 }{ -660 } = \cos(A) \]

Answer 18

And then calculate the left side . . .

Answer 19

+484

Answer 20

What do you mean?

Answer 21

144-225+484 over -660 =cosA

Answer 22

No, because you are subtracting "225" AND "484" from both sides... Thus, the numerator should be "144 - 225 - 484"

Answer 23

So, you are subtracting 225 from both sides and you are subtracting 484 from both sides.

Answer 24

ok :)

Answer 25

so the answer is 30.68

Answer 26

You mean the angle?

Answer 27

thats my final answer 30.68

Answer 28

You mean the size of the angle in degrees?

Answer 29

It's about that--I calculated that it was about 31.123 degrees... And remember, that's for angle A, the angle across from side "a", which we're assuming has length of 12 cm.

Answer 30

Anyway, you continue the same process with another side like so:

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

And then, when you have angle A & angle B, you can easily figure out the size of angle C because:

C = 180 - A - B

Answer 31

Make sense?

Answer 32

@Splash_Dance how

Answer 33

What?

Answer 34

Splash_Dance

Answer 35

Yes...

Answer 36

interior angle?

Answer 37

can i use herons law?

Answer 38

No, that's for calculating the Area of a triangle--you're just looking for the angles.