Question

Help please!! Geometry question

Answer 1

@hardlyhuman, welcome back to QC. Hope you're doing well today. How far did you get in your attempt to solve this one?

Answer 2

I narrowed down an answer based on what I physically saw.

Answer 3

And I'm doing alright, thank you. How are you?

Answer 4

I'm doing good, but I'm a little concerned about your problem solving approach here. Do you really think that physically observing this is more accurate than using the Law of Sines?

Answer 5

No of course not, I'm just gonna tell you straight up; I missed two years of math (7th and 8th) so I'm pretty much lost when it comes to this stuff.

Answer 6

Well, even if that is true, the law of sines is a very easy rule to apply here. The law of sines states that if you have a triangle with sides a, b, and c, and angles A, B, C, such at side a corresponds with Angle A, and side b corresponds with Angle B, and side c corresponds with Angle C then:

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

Answer 7

In this case we can say
side a = 10 which corresponds with Angle A = 31 degrees
side b = GH which corresponds with Angle B = 45 degrees

Answer 8

Then we can just use the proportion:
\(\dfrac{\sin(A)}{a} = \dfrac{\sin(B)}{b}\) and plug in those values to this formula. We won't need to use any values involving sides c and Angle C here.

Answer 9

If we plug in those given values, we'll end up with:
\(\dfrac{\sin(31^{\circ})}{10} = \dfrac{\sin(45^{\circ})}{GH}\)

Answer 10

Now all we have to do is re-arrange this so that we have \(GH = \text{ an equivalent expression to the one above}\)

Answer 11

Then we would simplify that expression using a calculator which would give us the value of side GH

Answer 12

Okay

Answer 13

@hardlyhuman what is the expression equivalent to side \(GH\)?

Answer 14

I don't know, I don't understand it

Answer 15

First we label the sides above which reflects what I wrote earlier:

In this case we let
side a = 10 which corresponds with Angle A = 31 degrees
side b = GH which corresponds with Angle B = 45 degrees

Answer 16

The arrows represent the correspondences between the angles and sides we will use in the Law of Sines formula.

Answer 17

Does this information help you?

Answer 18

yes thank you

Answer 19

So where are you stuck now?

Answer 20

Is it 13.7?

Answer 21

Yes, correct. You surprise me. Can you show the work you did to get that?

Answer 22

I did it on an online sketch board and I closed the window when I was done

Answer 23

Would you mind replicating your steps here. We have a drawing button below the comment box.

Answer 24

I actually gotta go, I have on site testing I need to get to before traffic hits. Thank you for the help though.