Question

Need a little bit of help with some trigonometry. Picture of problems follow.

Answer 1

I can't seem to completely wrap my head around this stuff. > . <

Answer 2

for #1, you should have a drawing like this

Answer 3

you use the law of sines to find the angle \(\LARGE \theta\)

Answer 4

Okay.

Answer 5

Law of sines

\[\Large \frac{\sin(\theta)}{b} = \frac{\sin(\alpha)}{a}\]

\[\Large \frac{\sin(\theta)}{2} = \frac{\sin(66)}{14}\]

do you see how to find \(\LARGE \theta\) ?

Answer 6

Just a sec, writing this down.

Answer 7

sin(theta)=.16437, sin-1(.16437)=9.4608?

Answer 8

incorrect

Answer 9

I thought so, how does one figure this out?

Answer 10

first off, hopefully you are in degree mode (not radian mode)

Answer 11

Yep, degree mode is active.

Answer 12

\[\Large \frac{\sin(\theta)}{2} = \frac{\sin(66)}{14}\]

\[\Large \sin(\theta) = 2*\frac{\sin(66)}{14}\]

\[\Large \sin(\theta) \approx 0.13050649\]

\[\Large \theta \approx \arcsin(0.13050649)\ \text{ or } \ \theta \approx 180-\arcsin(0.13050649)\]

\[\Large \theta \approx 7.49886163^{\circ}\ \text{ or } \ \theta \approx 172.501138^{\circ}\]

Those are the *possible* values of theta, you need to make sure they both work. So you go back to the original triangle and make sure that there is a possibility that all 3 angles add to 180 degrees (where none of the angles are negative numbers).

Answer 13

Let's say \(\Large \theta \approx 7.49886163\)

That would mean

\[\Large \theta + \alpha \approx 7.49886163+66 \approx 73.49886163\]

so the third unknown angle C is some angle such that \(\Large 0 < C < 180\) because the sum of theta and alpha is not over 180 degrees.

Answer 14

what I did wrong the first time around is inputting sin(66)*4, having them both there messed with the answer.

Answer 15

I see

Answer 16

I tried them separately and it worked out the same way yours did. XD

Answer 17

does the angle \[\Large \theta \approx 172.501138\] work?

Answer 18

No, because 172.501138 + 66 goes over 180.

Answer 19

yeah it means the third angle has to be negative in order to have the three angles add to 180 degrees

Answer 20

so the only possible value of theta is \[\Large \theta \approx 7.49886163^{\circ}\] meaning that only one triangle is possible

Answer 21

you will follow the same basic steps for #2 also

Answer 22

Okay, so start with the Law of sines.

Answer 23

correct

Answer 24

well you start with a drawing if you don't have one, but in this case they give it to you

Answer 25

\[\frac{ sinG }{\sin36} = \frac{ 29 }{ 25 }\]

Answer 26

\[sinG=\sin36*\frac{ 29 }{ 25}\]

Answer 27

G\[G =42.98688166, G \approx 43\]

Answer 28

I'm getting \[\Large G \approx 42.98681^{\circ}\] so yeah, roughly 43 degrees

Answer 29

If that's the case, then the answer to #2 is "c"
43 + 101 + 36 = 180

Answer 30

correct

Answer 31

Hooray, it makes sense now! (\> 6 <)/
Thank you ;-;

Answer 32

I'm glad it does