Find the length of one of the sides in a triangle

[TordKulen]

Hey!
I just started study landsurveying and got a task i don't figure out how to get the right answer. My goal is to find the length of one of the sides in a triangle, but i can not use pytagoras formula.

Here is the formula i am supposed to use (dont care about the text, its norwegian): http://i60.tinypic.com/nejknn.jpg

And here is the task:
"side a: 50,5845 gon (alfa), in degrees this is 45
side b: 1604,170m (gamma)
side c: 1128,620 m (beta)

Find the length of side a."

I know the answer is 1144,700m.

When i have tried i have found b2 and c2, then added those. After that i took b*2, multiplied with c. Then i took the answer from b2 and c2 added together and minus the answer from b*2 multiplied with c, and in the end i multiplied the cosinus of alfa.

Im from Norway and my english is not that good, but i hope that someone could help me out, or tell me what I've done wrong.

 

[HallsofIvy]

Hey!
I just started study landsurveying and got a task i don't figure out how to get the right answer. My goal is to find the length of one of the sides in a triangle, but i can not use pytagoras formula.

Here is the formula i am supposed to use (dont care about the text, its norwegian): http://i60.tinypic.com/nejknn.jpg

And here is the task:
"side a: 50,5845 gon (alfa), in degrees this is 45

So side a is 50.5846 m and the opposite angle, between sides b and c, is 45 degrees?

side b: 1604,170m (gamma)
side c: 1128,620 m (beta)

Find the length of side a."

I must have misunderstood. Didn't you just say that side a had length 50.5845 meters? Or is "gon" an angle measurement that is equal to 45 degrees?

If that is correct we can use the "cosine law" to find the length of side a:
a^2= b^2+ c^2- 2ab cos(\alpha)= (1604.170)^2+ (1128.620)^2- 2(1604.170)(1128.620)cos(45)

I know the answer is 1144,700m.

When i have tried i have found b2 and c2, then added those. After that i took b*2, multiplied with c. Then i took the answer from b2 and c2 added together and minus the answer from b*2 multiplied with c, and in the end i multiplied the cosinus of alfa.

This sounds like you are attempting the cosine law but it also sounds like you did (b^2+ c^2- 2bc)cos(\alpha). You multiply only the "2bc" by cos(\alpha), not the entire expression.

Im from Norway and my english is not that good, but i hope that someone could help me out, or tell me what I've done wrong.

 

[SteamKing]

The term 'gon' refers to an angular measure. In some countries, the 'gon' is also called the 'grad', where a circle is divided up into 400 grads and a right angle equals 100 grads:

http://en.wikipedia.org/wiki/Angle

The OP's angle alfa should therefore be 50.5845 gon * 90/100 = 45.526 degrees instead of 45 degrees.

 

[phinds]

This is a simple right triangle. I don't get where the "problem" is.

 

[SteamKing]

This is a simple right triangle. I don't get where the "problem" is.

The problem is the OP was apparently instructed not to use the Pythagorean Theorem, but to use the Law of Cosines instead.