Question

Use the Law of Sines. Find m 10 years ago

Answer 1

m<c?

Answer 2

yes, the measure of angle C.

Answer 3

@Nnesha @perl @Preetha

Answer 4

so we need ti find sin24

Answer 5

but it's not a right triangle.

Answer 6

does that still apply?

Answer 7

I don't understand the Law of Sines

Answer 8

yes it still apply just write sin24

Answer 9

okay

Answer 10

I got 0.4067....

Answer 11

@sparrow2

Answer 12

so just enter this in the formula and then round nearest tenth

Answer 13

what formula?

Answer 14

@perl

Answer 15

law of sines

Answer 16

I don't know the formula.

Answer 17

162/sinc=77/sin24

Answer 18

then find sinc and look at the table to the relevant angle

Answer 19

what table? and I'm very confused right now..

Answer 20

values of trig function at different angle

Answer 21

Does it make sense up to here
$$ \Large \frac{\sin 24^o}{77}= \frac{\sin C}{162} $$

Answer 22

why is it like that?

Answer 23

here is a diagram of the law of sines http://www.mathworksheetsgo.com/sheets/trigonometry/advanced/law-of-sines-and-cosines/images/picture-law-of-sines-formula.jpg

Answer 24

ohhhh, yes that makes sense.

Answer 25

so we are using just two parts of the three part ratio

Answer 26

you can do that since they are equal

Answer 27

okay.

Answer 28

we don't know `sin B` and `b` anyway at this point , yet

Answer 29

and we have to solve for C?

Answer 30

$$
\Large{
\frac{\sin 24^o}{77}= \frac{\sin C}{162}
\\~\\ \iff \\~\\
\sin 24^o \times 162 = 77 \times \sin C
\\~\\ \iff \\~\\
\frac{\sin 24^o \times 162}{77} = \sin C
}$$

Answer 31

okay. and how do we isolate C?

Answer 32

$$
\Large{
\frac{\sin 24^o}{77}= \frac{\sin C}{162}
\\~\\ \iff \\~\\
\sin 24^o \times 162 = 77 \times \sin C
\\~\\ \iff \\~\\
\frac{\sin 24^o \times 162}{77} = \sin C

\\~\\ \iff \\~\\
\sin^{-1} \left( \frac{\sin 24^o \times 162}{77} \right)= C

}$$

Answer 33

that's what I thought, okay.

Answer 34

make sure you are in degree mode if you are using a TI 83/84/85 calculator

Answer 35

I got 58.8

Answer 36

is that right?

Answer 37

yes :)

Answer 38

Oh, wow. Thank you so much! I might need your help later, but I don't know. \(\Huge\rlap{\tt\color{teal}{Thank~you!}}{\;\tt\color{lime}{Thank~you!}}\)

Answer 39

Now try to 'solve' the triangle (find all side lengths and angles).
You can find angle B using the fact that three angles of any triangle add up to 180.
Then use law of sines one more time to find side b, or alternatively you can use law of cosines

Answer 40

Your welcome :)