find the three lengths of a triangle with three angles given

[Qualinoshei]

ok, so i have a triangle with the angles 20, 40 and 120. the longest side is 10 cm longer than the shortest side. what are the three lengths?
^ i have tried so many methods, using the sine law or cosine law, giving variables but to no avail. i feel its really not as complex as its shown to be, but i really need help! plz and thank you

 

[Mrspi]

ok, so i have a triangle with the angles 20, 40 and 120. the longest side is 10 cm longer than the shortest side. what are the three lengths?
^ i have tried so many methods, using the sine law or cosine law, giving variables but to no avail. i feel its really not as complex as its shown to be, but i really need help! plz and thank you

Remember that the longest side of a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.

So, the shortest side is opposite the 20-degree angle. Let x = length of the shortest side.

The longest side is opposite the 120-degree angle. If the shortest side has length x, and the longest side is 10 cm longer than the shortest side, then length of longest side = x + 10.

Now, use the law of sines:

sin 20 / x = sin 120 / (x + 10)

You can solve that for x. Once you have x, you can get the longest and shortest sides....use the law of sines again to find the side opposite the 40-degree angle.

 

[Qualinoshei]

sin 20 / x = sin 120 / (x + 10)

i tried that but how do u rearrange it to solve for x?

 

[Mrspi]

sin 20 / x = sin 120 / (x + 10)

i tried that but how do u rearrange it to solve for x?

Cross-multiply:

sin 20 * (x + 10) = x*sin 120

x*sin 20 + 10*sin 20 = x*sin 120

Get all the terms containing x on one side.....

10 * sin 20 = x*sin 120 - x*sin 20

Factor "x" out of the two terms on the right side:

10*sin 20 = x(sin 120 - sin 20)

Now...can you finish?

 

[Qualinoshei]

oh thank you , yeah i got it !
oh if i may ask what level math do u think it is( as in grade level)?

 

[mmm4444bot]

… what level math do [you] think it is (as in grade level)?

From my point-of-view, introductory trigonometry is 8th-grade math because that's where I learned it.

(I don't know what junior high schools are teaching these days.)

 

[Mrspi]

Re:

… what level math do [you] think it is (as in grade level)?

From my point-of-view, introductory trigonometry is 8th-grade math because that's where I learned it.

(I don't know what junior high schools are teaching these days.)

Since this problem involves some "sort of" advanced trig (Law of Sines) which I have never seen presented below 10th grade, I'd say 10th grade geometry is about right.

While SOME 8th graders might be able to handle these concepts, my experience is that MOST don't.

I'm OLD, of course...so did not encounter trig until high school. I DO tutor students now, and I can tell you that most 8th graders are not ready to deal with abstract concepts. Maybe it's better to wait a year or two to deal with things like law of sines and law of cosines.....based on the fact that most of the 8th graders I see can't solve something as simple as 2x + 5 = 3x - 7


Just my opinion, of course.