104.5 degree triangle w/ 2 equal legs, need the 3rd leg's length

In summary, the conversation discusses finding the length of the third leg in a triangle with two known legs and an angle between them. The suggested solution is to use the cosine rule, which the person tried but did not get the correct answer. Another person suggests dividing the triangle into two right-angled triangles and using basic trigonometry to find the length of the third leg. The conversation ends with the person still expressing confusion about why the cosine rule did not work for them.
  • #1
CocoonOHorror
25
0

Homework Statement



i have a triangle with 2 legs of 96 inches. the angle between them is 104.5 degrees. how do i get the length of the 3rd leg?

Homework Equations

wish i knew.


The Attempt at a Solution


tried Cos, Sin, and Tan of 104.5 * length of a leg
 
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  • #3
Draw a line down the centre. Now you have two right-angled triangles. It should be a piece of cake from there.
 
  • #4
willem2 said:
How about the cosine rule?

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

works for unequal legs as well.

when i tried this i got 1.17545571, but the answer should be 1.5.

C^2=(.96)^2+(.96)^2-2(.96)(.96)(-.25038)
 
  • #5
DaveC426913 said:
Draw a line down the centre. Now you have two right-angled triangles. It should be a piece of cake from there.

thanks man! i think this worked, and i kind of understand why.

i still don't understand why the law of cosines didnt work for me, i wonder what i screwed up...
 
  • #6
CocoonOHorror said:
when i tried this i got 1.17545571, but the answer should be 1.5.

C^2=(.96)^2+(.96)^2-2(.96)(.96)(-.25038)

you forgot one of the minus signs in -2(.96)(.96)(-.25038)
 

1. What is the formula for finding the missing leg of a 104.5 degree triangle with 2 equal legs?

The formula for finding the missing leg of a triangle with two equal legs is c = a * √2, where c is the missing leg and a is the length of the known legs.

2. How do you determine the angle measurements of a 104.5 degree triangle with 2 equal legs?

The angle measurements of a triangle can be determined using the Pythagorean theorem, trigonometric functions, or the law of sines and cosines.

3. Is there a specific method for solving a 104.5 degree triangle with 2 equal legs?

Yes, you can use the Pythagorean theorem, trigonometric functions, or the law of sines and cosines to solve a 104.5 degree triangle with 2 equal legs.

4. What are the applications of a 104.5 degree triangle with 2 equal legs in real life?

104.5 degree triangles with 2 equal legs are often seen in architecture, engineering, and construction. They are also used in navigation and surveying.

5. Can a 104.5 degree triangle with 2 equal legs have more than one solution?

Yes, a triangle can have more than one solution depending on the given information and the methods used to solve it. It is important to check for extraneous solutions when using trigonometric functions.

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