Cap'n Refsmmat Posted June 5, 2008 Posted June 5, 2008 Is this a homework question or just a brainteaser? All you have to do is remember that the interior angles in a triangle add up to 180 degrees.
alan2here Posted June 5, 2008 Posted June 5, 2008 (edited) How totally careless of me, ignore this post 3x + 4x + 5x = 180 find x 12x = 180 x = 180 / 12 x = ? Edited June 6, 2008 by alan2here
Bignose Posted June 5, 2008 Posted June 5, 2008 (edited) 3x + 4x + 5x = 180 Ummmmm, no. 3x + 4x + (5x + something) = 180. This is along the right idea -- using the sum of the internal angles must be equal to 180 degrees -- but 5x isn't the entire angle of the top of the large triangle. Using the idea that the angles of a triangle must add to 180 you can write a bunch of equations. Also, the angles along a straight line (not so subtle hint, that'd be angle ABD and angle BDC) also add to 180. Write out all the equations for the triangle and the straight line and you should have more than enough equations to determine any unknowns. Edited June 5, 2008 by Bignose
ydoaPs Posted June 6, 2008 Posted June 6, 2008 You can use the fact that the line makes two triangles to help you.
alan2here Posted June 6, 2008 Posted June 6, 2008 3x + 4x + 5x + n = 180 12x + n = 180 (x + n = 180 / 12?) 3x + 5x + n = 180 8x + n = 180 4x + n + o = 180 I'm a little stuck here as well
ydoaPs Posted June 6, 2008 Posted June 6, 2008 3x + 4x + 5x + n = 18012x + n = 180 (x + n = 180 / 12?) You made a math error here. Also, don't the angles add up to 360 degrees? 3x + 5x + n = 180 8x + n = 180 4x + n + o = 180 I'm a little stuck here as well Remember that since the line makes two triangles out of one, you now have three triangles. Since there are two unknowns, I made a system of three equations with each equation relating the angles of a triangle. I then solved the system of equations for x using the substitution method.
Cap'n Refsmmat Posted June 6, 2008 Posted June 6, 2008 You made a math error here. Also, don't the angles add up to 360 degrees? The angles of a triangle add up to 180 degrees.
ydoaPs Posted June 6, 2008 Posted June 6, 2008 The angles of a triangle add up to 180 degrees. That depends on the geometry you're using! Either way, my method still works.
Bignose Posted June 6, 2008 Posted June 6, 2008 4 equations 4 unknowns: right most small triangle: 5x + 3x + BDC = 180 left most small triangle: 4x + ABD + ADB = 180 large triangle: 4x + ABD + 5x + 3x = 180 line: ADB + BDC = 180 Now it's just equation solving... ------------------------- I have a small side question based on the original question of the OP. Would knowing that a triangle has 180 degrees be something known "without trig" I mean, trig obviously knows that 180 degrees is special -- sin(180 degrees) = 0, cos(180 degrees) = -1, etc. But, is that 180 degrees something known without trig? To a certain extent, didn't trig help define exactly what a degree, and what a radian is? I don't know the history of math well enough.... these are just ponderances of mine.
Bignose Posted June 7, 2008 Posted June 7, 2008 Here's how you do 2 equations with 2 unknowns: As an example, let's look at: x+y = 7.2 3x-2y = 10.6 Rearrange one of the equations to isolate a variable. I'm going to do the first equation: y = 7.2-x Now, plug this definition of y into the second equation: 3x -2(7.2-x) = 10.6 And solve for x Then, with the solution for x, you can compute y = 7.2-x You should do this and find that x=5 and y =2.2 Note that the choices are completely arbitrary. I could have used x = 7.2-y as the rearrangement. Or, I could have used the second equation. x = (1/3)*(2y + 10.6) or y = (1/2)*(-10.6+3x) Now, 4 equations with 4 unknowns is exactly the same. You just have to repeat it a lot more times. And be careful to write down every step and be accurate to make sure the results are correct.
Anubisboy Posted June 10, 2008 Posted June 10, 2008 Bignose, I may be making a mistake, but after solving the equations you provided, I didn't get obtain a result for [math]x[/math]. Equation one implies [math] BDC=180-8x[/math], and equation three implies [math]ABD=180-12x[/math]. Substituting the result from equation 3 into equation 2 gives [math]4x+ADB+180-12x=180 \Longrightarrow ADB=8x[/math]. Substituting the result for [math]ABD[/math] plus the result obtained for [math]BDC[/math] into equation four yields [math] 180-8x+8x=180 \Longrightarrow 180=180[/math], which, while true, is not very revealing. I think one must make use of the fact that [math]AB=CD[/math]. How this is done is not readily apparent to me. Anubisboy
Bignose Posted June 13, 2008 Posted June 13, 2008 Anubis boy, you are right. The 4 equations aren't linearly independent... I too get only trivial results from it -- angles equal to 0 and 180. I don't have a tremendous amount of time to think on this right now, but I'm going to keep mulling it over...
Anubisboy Posted June 13, 2008 Posted June 13, 2008 Following the link located at the lower left hand corner of the diagram, I found the problem at this site as well. ([url=http://www.gogeometry.com/problem/problem013.htm][/url]http://www.gogeometry.com/problem/problem013.htm). However, the description of the problem doesn't completely match the diagram for the problem. There must be an error in either the diagram or description.
DeanK2 Posted June 20, 2008 Posted June 20, 2008 [math]BDC=180-8x[/math] [math]ABD=180-12x[/math] [math]0<x< 15[/math] [math]20x+ABD+BDC=360; =>...ABD+BDC > 60...if...0<x<15[/math] With the limits above, x can be found. A simple logarithm would suffice.
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now