Question

the angles of a triangle are in the ratio 2:3:5. if the biggest side is 35cm

Answer 1

@AllTehMaffs

Answer 2

the biggest is 35, therefore the smallest is 14, and the middle is 21

Answer 3

@AllTehMaffs

Answer 4

find the measures of all the angles?

Answer 5

for all angles use law of cosines

\[c^2=a^2+b^2-2ab \cos C\]
\[a^2=c^2+b^2-2cb \cos A\]
\[b^2=a^2+c^2-2ac \cos B\]

Solve for the angles

Answer 6

how?

Answer 7

Can you get cos C by itself in the first equation?

Answer 8

yup

Answer 9

Then you found C

Answer 10

C=35?

Answer 11

no, side c = 35

and C is different.

Answer 12

the angles of a triangle are in the ratio 2:3:5. if the biggest side is 35cm

Answer 13

35cm isn't an angle

Answer 14

a=21 b=14?

Answer 15

those are the side lengths

Answer 16

so what is the measures of all angles?

Answer 17

how can i get the measures of the all angles?

Answer 18

The Law of Cosines, like I wrote above

\[c^2=a^2+b^2-2ab \cos C\]
\[c^2-a^2-b^2=-2ab \cos C\]
\[ \cos C = \frac{c^2-a^2-b^2}{-2ab}\]
\[C = \arccos \Bigg(\frac{c^2-a^2-b^2}{-2ab} \Bigg) \]

Answer 19

you do that for 2 of the angles, and can figure out the third through subtracting from 180º

Answer 20

arccos?

Answer 21

or inverse cosine

on calculators it's sometimes written as
\[cos^{-1}\]

Answer 22

ok i solve it

Answer 23

C=180