Question

Solve triangle UVW if m angle U = 41°, w = 12, and v = 13.

A) m angle U = 41°, m angle V ≈ 75.7°, m angle W≈ 63.3°, and u ≈ 8.8, v = 13, and w = 12

B) m angle U = 41°, m angle V ≈ 63.3°, m angle W ≈ 75.7°, and u ≈ 9.9, v = 13, and w = 12

C) m angle U = 41°, m angle V ≈ 63.3°, m angle W ≈ 75.7°, and u ≈ 8.8, v = 13, and w = 12

D) m angle U = 75.7°, m angle V ≈ 41°, m angle W ≈ 63.3°, and u ≈ 8.8, v = 12, and w = 13

Answer 1

@Jamierox4ev3r

Answer 2

wow this involves a lot of work lol hold on :P

Answer 3

sorry lol i just dont understand it

Answer 4

its basically the same process as the other problems we've done. It just involves solving for more things T_T

Answer 5

yea.. :/

Answer 6

I'm just going to change uvw to abc if you don't mind...makes things easier for me

Answer 7

yea thats fine

Answer 8

alright wow this problem though...tedious as heck!

btw, we can eliminate option D right off the bat, it contradicts the first part of the problem lol

Answer 9

\[u=\sqrt{w^2+v^2-2wvcos(U)}\]

Answer 10

you can solve for side a (or u) first

Answer 11

12^2 +13^2 - 2(12)(13)cos(U)

Answer 12

yep! and once you solve the side, you can possibly switch to law of sines if you so choose to find the rest!

Answer 13

I actually have to go really soon, its really late for me ;-;

Answer 14

ok just 1 more min plz

Answer 15

144 + 169 - 312 = 6

Answer 16

and...she leaves me :/

Answer 17

i got no answer :c

Answer 18

@TheSmartOne

Answer 19

@Michele_Laino

Answer 20

@Jhannybean

Answer 21

I haven't learned this yet :/

Maybe @Jhannybean @Michele_Laino @perl @Miracrown can help you :)

Answer 22

Please I apply the Carnot Theorem, so I get:
\[{u^2} = {v^2} + {w^2} - 2vw\cos 41 = 169 + 144 - 312\cos 41\]
what is u?

Answer 23

angle U = 41 degrees

Answer 24

yes!

Answer 25

ok so whats next

Answer 26

next please you have to perform the computation, namely:
\[{u^2} = 169 + 144 - 312\cos 41 = 313 - 312 \cdot 0.755 = 313 - 235.6 = 77.4\]

Answer 27

so we have:
\[{u^2} = 77.4\]

Answer 28

ok but in the choices its 75.7

Answer 29

please you have to look at the values for u

Answer 30

so you have to compute this:
\[u = \sqrt {77.4} = ...?\]

Answer 31

ohh so it would be 8.7

Answer 32

I think 8.8 since you have to round off your result

Answer 33

yea true

Answer 34

ok so now we should find v

Answer 35

please note that in order to find V, you can apply the sines Theorem

Answer 36

namely:
\[\frac{v}{{\sin V}} = \frac{u}{{\sin 41}}\]

Answer 37

and substituting the values for u and v, we get:
\[\frac{{13}}{{\sin V}} = \frac{{8.8}}{{\sin 41}}\]

Answer 38

next you have to solve that equation for sinV, so I can re-write it as follows:
\[\sin V = \frac{{13}}{{8.8}}\sin 41\]

Answer 39

please, what is sinV?

Answer 40

would it be 1.32

Answer 41

no, I don't think since sinV has to be a number less than 1

Answer 42

hint:
\[inV = \frac{{13}}{{8.8}}\sin 41 = \frac{{13}}{{8.8}} \cdot 0.656 = ...?\]

Answer 43

oops...
\[\sin V = \frac{{13}}{{8.8}}\sin 41 = \frac{{13}}{{8.8}} \cdot 0.656 = ...?\]

Answer 44

0.96

Answer 45

ok!

Answer 46

so what is V?

Answer 47

please you have to use your scientific calculator

Answer 48

i dont know how to get v

Answer 49

please you have to use the inverse function option, nevertheless here i your value for V:
V=73.74 degrees, namely:
V = 74 degrees

Answer 50

oops... here is your value...

Answer 51

oh ok so i think the answer would be A

Answer 52

yes! That's right!

Answer 53

ok thanks for your help :)

Answer 54

thank you! :)