# Find the length of one of the sides in a triangle

1. Aug 26, 2014

### TordKulen

Hey!
I just started study landsurveying and got a task i dont figure out how to get the right answer. My goal is to find the lenght 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

"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.

2. Aug 26, 2014

### HallsofIvy

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

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:
$$a^2= b^2+ c^2- 2ab cos(\alpha)= (1604.170)^2+ (1128.620)^2- 2(1604.170)(1128.620)cos(45)$$

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.

3. Aug 26, 2014

### SteamKing

Staff Emeritus
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.

4. Aug 26, 2014

### phinds

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

5. Aug 26, 2014

### SteamKing

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