The obscure triangle has side lengths of 16 in, 13 in, and 20 in. I am assuming side a is 13, side b is 16, and side c is 20. We are looking for angle x between side a and side b. I have tried to use the formula for cos(C) because angle C is supposed to be between side b and side a. However, it is not coming out to any of the answer choices. My work is down below.

cos(C)=(a^2+b^2-c^2)/(2ab)
=(13^2+16^2-20^2)/(2*13*16)
=(169+256-400)/(416)
=25/416
=0.06009615384
cos(C)=3.44325598 degrees

The answer choices are:
a. 14
b. 40
c. 53
d. 86

I also tried cos(A) and cos(B) just to see if I was wrong, but they also did not come out to any of the answer choices.

cos(A)=(b^2+c^2-a^2)/(2bc)
=(16^2+20^2-13^2)/(2*16*20)
=(256+400-169)/(640)
=487/640
=0.7609375
cos(A)=43.6 degrees

cos(B)=(a^2+c^2-b^2)/(2ac)
=(13^2+20^2-16^2)/(2*13*20)
=(169+400-256)/(2*13*20)
=313/520
=0.60192307692
cos(B)=34.48765.... degrees

I am completely and utterly confused. Thank you!

Law of Cosines Practice:

1. (D): 87
2. (B): 16.9
3. (A): 40.0 degrees
4. (B): 25.4 ft.
Law of Cosines Quick Check:
1. (A): 1.7
2. (D): 64.4
3. (A, E, F): 140, 24, & 16(in order.)
4. (C): 106 mi.

I don't know how you did this step:

cos(C)=0.06009615384
cos(C)=3.44325598 degrees

It should immediately have raised a "what?" flag. You know that cos(90)=0, so C should be close to 90. You did C=arcsin(0.06009)
So, you not only pushed the wring button, you mislabeled it as cos(C) rather than C.

Hi Steve. Sorry, but I have read over what you said a couple times but I am still confused. How did I mislabel it as cos(C) rather than C?

You typed:

cos(C)=0.06009615384
cos(C)=3.44325598 degrees

You should have typed
I don't know how you did this step:
cos(C)=0.06009615384
C=3.44325598 degrees BUT still wrong, that is sin, not cos
cos^-1 (0.06) = about 86.6 degrees

Well, it seems like you're stuck in a triangle of confusion! Don't worry, I'm here to bring some humor to the rescue!

Looks like you've been playing a game of Cos and Seek, but the answers seem to be hiding from you. Now, let's take a step back and have a closer look at that triangle. Remember, triangles can sometimes be a little sneaky, especially when it comes to those pesky angles.

To find angle x, you can use the Law of Cosines. But I think I know why your calculations aren't matching the answer choices. It seems like you might have made a tiny mistake in determining side a, b, and c.

Let me set the record straight for you. In this case, side c has the length of 20 inches, side b has the length of 16 inches, and side a has the length of 13 inches. So, let's give the triangle its proper identity.

Now, you can go ahead and use the Law of Cosines again, but with the correct values this time. Remember, cos(C) = (a^2 + b^2 - c^2) / (2ab).

cos(C) = (13^2 + 16^2 - 20^2) / (2 * 13 * 16)
= (169 + 256 - 400) / (416)
= 25 / 416
≈ 0.0601

Ah, that sneaky angle! It turns out that cos(C) is not in degrees but in decimal form. So, you'll need to use the inverse cosine function (cos⁻¹) to find the actual angle.

cos⁻¹(0.0601) ≈ 86°

Hooray, that's it! The angle x, or angle C, measures approximately 86 degrees. So the answer choice you're looking for is option d. 86!

Triangles can be quite twisted, but with a little humor and a fresh perspective, you can untangle the mysteries and solve the problem. Keep up the good work!

It appears that you have made a small calculation mistake in your calculations for cos(C). The correct value of cos(C) should be:

cos(C) = (a^2 + b^2 - c^2) / (2ab)
= (13^2 + 16^2 - 20^2) / (2 * 13 * 16)
= (169 + 256 - 400) / (416)
= 25 / 416
≈ 0.06009615385

However, to find the angle x between side a and side b, you need to use the inverse cosine function (cos^(-1)) to find the angle from its cosine value. So the correct calculation is:

x = cos^(-1)(cos(C))
≈ cos^(-1)(0.06009615385)
≈ 89.0759 degrees

Therefore, the angle x is approximately 89.08 degrees. However, this doesn't match any of the answer choices given (a, b, c, d). It is possible that there could be a typo in the answer choices or a mistake in the question itself.

I would recommend double-checking the question, answer choices, and calculations to ensure accuracy. If you're still unable to find the correct answer, it could be worth consulting the original source or seeking additional assistance.