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Mathematics 15 Online
zarkam21:

For questions 5 - 6, solve for the remaining angles.

zarkam21:

1 attachment
Vocaloid:

since we don't have any angles we have to use law of cosines pick a side (let's use c i guess) and solve for angle C

zarkam21:

c²=a²+b²-2abCos(C)

Vocaloid:

yup then plug in a, b, c

zarkam21:

a=255 b=270 c=442.85

Vocaloid:

hold on a sec

zarkam21:

okay

Vocaloid:

|dw:1526059303865:dw|

Vocaloid:

be careful with your labels a = 270 b = 442.85 c = 255

zarkam21:

yeah thats where i was confused

Vocaloid:

just remember that a is across from angle A, b is across from B, etc.

zarkam21:

c²=a²+b²-2abCos(C) 225^2=270^2+442.85^2-2*270*442.85 ((Cos(C)

zarkam21:

are there supposed to be 2 solutions?

Vocaloid:

there should only be 1

Vocaloid:

sometimes software can get a little confused, try solving for cos(x) then take the arcsin of the result

Vocaloid:

*arccos

zarkam21:

0.91

Vocaloid:

good, then take the arccos of that to get the angle

zarkam21:

24.49 degrees

Vocaloid:

awesome, then repeat the process for one of the other angles (A or B)

zarkam21:

a²=b²+c²-2bc Cos(A) 270^2=442.85^2+225^2-2*442.85*225.2 ((Cos(A) 0.87 ----> 0.52(A)

Vocaloid:

make sure that your calculator/whatever is in degrees mode not radians arccos(0.87) = 29.36 degrees then it's just 180 - angle A - angle C = angle B to find angle B

zarkam21:

180-24.49-29.36=126.15 degrees(B)

Vocaloid:

good, so that's 5 done, repeat the steps for triangle 6

zarkam21:

A=15 B=15 C=19

zarkam21:

just confirming the sides the rest i will attempt by myself

Vocaloid:

switch a and c

zarkam21:

okay im doing it now will post it once im finished

zarkam21:

is this right for C

zarkam21:

c²=a²+b²-2abCos(C) 15^2=19^2+15^2-2*19*15 ((Cos(C) arccos(19)---->208.6 degrees ©

Vocaloid:

cosC = 19/30 not just 19 so arccos(19/30) = ?

zarkam21:

50.7

Vocaloid:

good, now try solving for angle A or angle B using the same method

zarkam21:

a²=b²+c²-2bc Cos(A) 19^2=15^2+15^2-2*15*15 ((Cos(A) arccos(361) =

zarkam21:

is 361 right?

Vocaloid:

I got something a little diff cos(A) = 89/450 A = ?

zarkam21:

5

Vocaloid:

what is arccos(89/450) = ?

zarkam21:

78.59

zarkam21:

that would be for A

Vocaloid:

good, now we have angle A and C, just gotta solve for angle B and we're done

zarkam21:

then: 180-78.59-50.7=50.71

zarkam21:

and that would be angle B

Vocaloid:

good, that's both our triangles solved

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