Question

@iGreen

Answer 1

Just a min, let me get to the questions

Answer 2

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

C = 67 degrees, a = 21, c = 20

A = 14.9, B = 98.1, b = 21.5; A = 165.1, B = 81.9, b = 21.5
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
A = 14.9, B = 98.1, b = 18.6; A = 165.1, B = 81.9, b = 18.6

Answer 3

Is there a picture?

Answer 4

no

Answer 5

I'm not sure what this is supposed to be for:

C = 67 degrees, a = 21, c = 20

Is it like angle measurements for a triangle?

Answer 6

Oh..wait..hold on..give me a minute.

Answer 7

Okay, we can use the rule:

\(\sf \dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} = \dfrac{c}{sin(C)}\)

Answer 8

just a min doing an interview rn

Answer 9

ok im back

Answer 10

So we can set up a proportion.

We know that

\(\sf \dfrac{sin(A)}{a} = \dfrac{sin(C)}{c}\)

So we can plug in what we know:

\(\sf \dfrac{sin(A)}{21} = \dfrac{sin(67)}{20}\)

So:

\(\sf A = arcsin(\dfrac{21sin(67)}{20})\)

We can plug this into our calculator:

http://www.wolframalpha.com/input/?i=arcsin%2821sin%2867%29%2F20%29

Which gives us approximately \(\sf 75.13^o\).

So we have two Angle measurements, A(\(\sf 75.13^o\)) and C(\(\sf 67^o\)), now we can easily find the last one by adding these together and subtracting that from 180. What do you get? @sleepyjess

Answer 11

37.87

Answer 12

Yep, so angle B is \(\sf 37.87^o\).

Answer 13

Now we have to find 'b'..because there are two options that have the same 3 angle measurements..but 'b' is different in both of those options.

We can use the same rule:

\(\sf \dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} = \dfrac{c}{sin(C)}\)

Let's take \(\sf \dfrac{c}{sin(C)}\), and plug in what we know:

\(\sf \dfrac{c}{sin(C)} \rightarrow \dfrac{20}{sin(67^o)} \rightarrow \dfrac{20}{0.920504853} \rightarrow~?\)

Divide that.

Answer 14

@sleepyjess

Answer 15

\(\sf\approx 21.73\)

Answer 16

Right, so we know that \(\sf \dfrac{c}{sin(C)} \approx 21.73\), that means \(\sf \dfrac{b}{sin(B)}\) also equals \(\sf 21.73\).

So we can write: \(\sf \dfrac{b}{sin(B)} = 21.73\)

We already know what B is, so we can plug that in and solve for 'b'. \(\sf \dfrac{b}{sin(37.87^o)} = 21.73\).

Can you solve that for 'b'? Just find the sine of 37.87 degrees and then multiply that to both sides..

Answer 17

What did you get? @sleepyjess

Answer 18

sorry, had to go get my calculator

Answer 19

\(\approx 3.7\)

Answer 20

Actually I got something else..lol

Answer 21

:(

Answer 22

What's sin(37.87 degrees)?

Answer 23

\(\approx .17\)

Answer 24

No..that's sine 37.87..you have to put in the degrees.

Answer 25

\(\sf sin(37.87) \neq sin(37.87^o)\)

Answer 26

.614?

Answer 27

Yep..now multiply that to both sides..

\(\sf \dfrac{b}{0.614} = 21.73\)

Answer 28

13.34

Answer 29

Yep, and option B has b = 13.3..so that's our answer.

Answer 30

Yay! Thank you so much! :D

Answer 31

No problem.