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

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.

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HallsofIvy
Homework Helper
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
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
Staff Emeritus
Homework Helper
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
Gold Member
2019 Award
This is a simple right triangle. I don't get where the "problem" is.

SteamKing
Staff Emeritus