Find the length of one of the sides in a triangle

However, their calculations seem to be incorrect, so they are asking for help or clarification on where they went wrong.
  • #1
TordKulen
1
0
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.
 
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  • #2
TordKulen said:
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:
[tex]a^2= b^2+ c^2- 2ab cos(\alpha)= (1604.170)^2+ (1128.620)^2- 2(1604.170)(1128.620)cos(45)[/tex]

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 [itex](b^2+ c^2- 2bc)cos(\alpha)[/itex]. You multiply only the "[itex]2bc[/itex]" by [itex]cos(\alpha)[/itex], 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.
 
  • #3
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
This is a simple right triangle. I don't get where the "problem" is.
 
  • #5
phinds said:
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.
 

1. What is the Pythagorean Theorem and how is it used to find the length of a side in a triangle?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as a formula: a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides. This theorem can be used to find the length of a side in a right triangle when the lengths of the other two sides are known.

2. What is the formula for finding the length of a side in a triangle using the Law of Sines?

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is equal to the same ratio for the other two sides and their opposite angles. This can be written as a formula: a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the lengths of the sides and A, B, and C are the opposite angles. This formula can be used to find the length of a side in any triangle when the measures of two angles and one side are known.

3. Can you use the Law of Cosines to find the length of a side in a triangle?

Yes, the Law of Cosines can be used to find the length of a side in a triangle when the measures of two sides and the included angle are known. The formula is c² = a² + b² - 2ab cos(C), where c is the length of the side opposite the included angle and a and b are the lengths of the other two sides.

4. How do you find the length of a side in an equilateral triangle if you only know the perimeter?

An equilateral triangle has three equal sides, so to find the length of one side, you can divide the perimeter by 3. For example, if the perimeter is 15 units, each side would be 15/3 = 5 units long.

5. Is it possible to find the length of a side in a triangle if you only know the lengths of two sides and the angle between them?

Yes, this can be done using the Law of Cosines. The formula is c² = a² + b² - 2ab cos(C), where c is the length of the side opposite the included angle and a and b are the lengths of the other two sides. However, if you only know two sides and the angle opposite one of them, there may be two possible solutions, so more information is needed to determine a unique solution.

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