Question

Trigonometry question. Find the measure of angle x.

Answer 1

I would like to learn instead of just an answer.

Answer 2

Hello, OM!!
Glad you like my new photo, courtesy of @thomaster.
You have a "right triangle" here, meaning that one of the angles of the triangle is 90 degrees. In cases like this, when you have the hypotenuse and the length of one leg, you can easiy find the length of the other leg, using the Pythagorean Theorem. How familiar does that sound?

Answer 3

Very, let me do that first.

Answer 4

The length of the third side is ... ??

Answer 5

5.65685424949 I got this.

Answer 6

What would I do now.

Answer 7

Looks good! Our goal is to find the measure of that angle x. You could use the Law of Sines, for one. Or you could use the Law of Cosines, now that you have the length of the 3rd side. Which sounds more familiar to you?

Answer 8

None really, I'm just now learning trigonometry.

Answer 9

Are you better with ratios or better with square roots?

Answer 10

I can do square roots and ratios. But, am better with square roots.

Answer 11

OK: Let's use the Law of Cosines in this case.

Would you please label the sides of the given triangle. Call the side of length 7 "a", the side with length 5.659 "b" and the hypotenuse "c", OK?

Answer 12

Here's the form of the Law of Cosines that we'll use (there are three forms):\[a^2=b^2+c^2-2ab~\cos A\]

Answer 13

It'd be well worth writing this down, with the label "Law of Cosines."

Answer 14

Now it happens that side a (which is 7 in our problem) is opposite angle A, which is angle x in our problem. OK with that? It's just a naming convention.

Answer 15

As you have seen, side a has length 7. Our goal is to find Angle A, which is the same as Angle x. OK?

Answer 16

Awaiting your response before typing anything else.

Answer 17

OK. I saw what all you typed. I am SO sorry, but I had an emergency that I had to take care of.

Answer 18

\[a^2=b^2+c^2-2bc*\cos A,~ or~b^2+c^2-2bc*\cos x\]

Answer 19

Opposite the unknown angle A (or x) is the side " a ", which has length 7.
Thus, we get\[7^2=b^2+c^2-2bc*\cos A,~ or~b^2+c^2-2bc*\cos x\]

Answer 20

The other 2 sides are 9 and 5.569. Just substitute those for b and c and calculate cos x.

Answer 21

\[7^{2}=5.659^{2}+9^{2}-2 \times 5.659 \times9 \times cosA\]Is this what it looks like then?

Answer 22

Yes! That's excellent! By evaluating this, you'd get an equation that says "so and so equals cos A" and then you'd need to use the inverse cosine function to find the angle A.
Have you done any of this work before?

Answer 23

No.

Answer 24

Do evaluate this equation as best you can. It will look like this:
\[7^{2}=5.659^{2}+9^{2}-2 \times 5.659 \times9 \times cosA\]

Answer 25

\[49=5.659^{2}+81-2 \times 5.659 \times9 \times cosA\]

Answer 26

Try finishing it. I'll be back to help you if there are any problem.s

Answer 27

ok

Answer 28

\[49=32.024+81-2*5.659*9*cosA\] I got 49. Is the measure of the angle 49?

Answer 29

I need to do some quick calculations. I'll be right with you.

Answer 30

Here's what I'm getting:
49 = 113.024 - 101.862 cos A

Answer 31

I'm going to rush through the solution and then come back to answer any questions.
49-113.024=-101.862 cos A

Answer 32

ok

Answer 33

-64.024=-101.862 Cos A

Divide both sides by -101.862. This is the cosine of A. Find A.

Answer 34

I got 0.6285=CosA?

Answer 35

sorry, had trouble with OpenStudy's software.

Use your calculator to find angle A, given that the cosine of angle A is 0.6285. I will explain the procedure if need be.

Answer 36

Yeah, I don't know how to put it in my calculator.

Answer 37

I get the result 51.06 degrees.

What kind of calculator have you?

Answer 38

My other one is lost, and I can't remember what it is, but I don't know if google would work.

Answer 39

Nothing to be lost by trying google. Type this into Google: arccos 0.6285.

Answer 40

I've just done that and have gotten a result...but the result is in radians. Do you know how to convert radians to degrees? 0.891 radians is equivalent to my 51.06 degrees.

Answer 41

I don't know how to convert radians to degrees, but I just put in degrees after the arcos 0.6285 and it gave me he 51.06

Answer 42

"in degrees"

Answer 43

So the measure of the angle to the nearest degree would be 51 right?

Answer 44

I haven't checked our work, but do think that that sounds very reasonable.
I urge you to take notes on what we did here, as well as to try more problems of the same kind for the additional practice. I can easily guide you through that, but not now, unfortunately, as I'm helping another student with a different problem. Greatly enjoyed working with you!

Answer 45

I will save this as a bookmark and reference with it often, and I thank you so much for helping me. I admire the fact that you didn't give up on me. Thank you very much.