Question

Please help! Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

C = 67°, a = 21, c = 20

Answer 1

The Law of Sines :
a/sinA = c/sinC

Answer 2

or sinA = (a sinC / c)

Answer 3

just put the values of them, giving us :
sinA = 21*sin67° / 20 = .... (use the calculator to get sin67°)

Answer 4

I got .966

Answer 5

finally, after u got the value of sinA, take the arcus sin to get the measure of A

Answer 6

do you mean arcos?

Answer 7

sinA = 0.966
A = arc(sin(0.966) = ... (use the calculator again :))

Answer 8

got it ?

Answer 9

umm, do I use arcos and then sin?

Answer 10

it is the value of sines, why we use arcos ??

Answer 11

I got 75 using arcsin(.966) but i dont think thats right

Answer 12

yes, that's right
(nearest)

Answer 13

but, dont ferget the identity of :
sin (180 - x) = sin x
so, sin75 = sin (180-75) = sin105
therefore there are 2 values of A satisfies, are
A = 75 or A = 105 degrees

Answer 14

* forget

Answer 15

so how do I decide which answer is correct?
A = 75.1°, B = 37.9°, b = 13.3; A = 104.9°, B = 8.1°, b = 3.1
A = 75.1°, B = 37.9°, b = 30; A = 104.9°, B = 8.1°, b = 30

Answer 16

ah, ur option wants the nearest of A=75.1

Answer 17

so, if there are 2 measures of A=76.1 and C=67, to get B :
B=180-(76.1+67) = 180 - 143.1 = 36.9 degrees

Answer 18

looks no option there, haha

Answer 19

oppss, i do mistake it should 75.1 not 76.1 :)

Answer 20

let's try again :
B = 180 - (75.1+67) = 180 - 142.1 = 37.9 degrees

Answer 21

and because there are 2 values of A, are A=75.1 and
from sin (180 - x) = sin x
so, sin75.1 = sin (180-75.1) = sin104.9
thus, A=104.9 deg

Answer 22

to get B :
B=180-(67+104.9)
B=180-171.9 = 8.1 degrees

Answer 23

SOLVED

Answer 24

but does b= 13.3 or 30?

Answer 25

ah, the length of b right ? sorry, it's left

Answer 26

use the law of sines again
a/sinA = b/sinB or
b = a*sinB/sinA = ...
just put the values of a, sinB, and sinA
(dont forget there are are 2 the values of A, so will get 2 values of B too)

Answer 27

try it ...

Answer 28

whats the value of a again?

Answer 29

it's given in ur question above :P

Answer 30

oh 21 okay

Answer 31

a is the length of side, but
A is the measure of angle A
they are different

Answer 32

I understand, I got b = 13.3

Answer 33

So it would be the first option i had given

Answer 34

the 2nd ?

Answer 35

no, b = 30 in the 2nd option...

Answer 36

nevermind, exactly the 2nd is 3.1 right ?

Answer 37

i mean the value for b

Answer 38

oh yes, thats correct

Answer 39

okay, game is over

Answer 40

can you help me answer a much simpler question quickly/

Answer 41

the new question ?

Answer 42

State whether the given measurements determine zero, one, or two triangles.

A = 61°, a = 23, b = 24