I cannot do the math

[Cpt shakes]

I have tried and I cannot reteach myself the math. Hopefully, someone on here can. If you have two aluminum tubes. Each one is 38 inches long. If you connect the end of each one to the other and separate them at the other end by 120 degrees, what is the distance in inches between the ends of the two tubes?

 

[Robb]

68.818 inches

http://www.calculator.net/triangle-...x=38&vy=38&va=&vz=&vb=&angleunits=d&x=90&y=18

 

[Shadetree Mechanic]

I can't remember how to do this either. I am looking up the law of cosine now.

 

[HomerBB]

Well, just make sure the Cosine cop is at the donut shop if you break that law. . .

 

[Shadetree Mechanic]

I think I found it.

https://www.ck12.org/book/CK-12-Interactive-Geometry-for-CCSS/section/7.7/

Notice that in this triangle, the included angle is obtuse. As was explained earlier, the Law of Cosines works for acute, right, and obtuse angles. The names of the sides do not match a,b , and c from the Law of Cosines exactly. What is important is that the angle you choose for ∠C is the included angle of the two sides you choose for a and b . Side c is opposite ∠C .

In this triangle, the sides 18 and 14 have an included angle of 122 ∘ . x is opposite the 122 ∘ angle. Use the Law of Cosines to relate these 4 values.

18 2 +14 2 −2(18)(14)cos122 ∘ 324+196+267.08787.08x =x 2 =x 2 =x 2 ≈28.05

 

[Captain Kilowatt]

68.818 inches

http://www.calculator.net/triangle-...x=38&vy=38&va=&vz=&vb=&angleunits=d&x=90&y=18

That formula says 65.818 inches not 68.818.

 

[Robb]

That formula says 65.818 inches not 68.818.

Yeah forgot to put on my reading glasses. My mistake. But I'd remembered that all you need is side/angle/side to get the answer; or close enough to it to get the hypotenuse. The calculator did all of the heavy lifting.