Comments on: Making them think http://blog.mathsage.com/?p=538 Where Mr. K shares about learning about learning. Thu, 26 Aug 2010 05:29:40 +0000 hourly 1 http://wordpress.org/?v=3.0.1 By: Mr. K http://blog.mathsage.com/?p=538#comment-447 Mr. K Wed, 11 Feb 2009 01:33:16 +0000 http://blog.mathsage.com/?p=538#comment-447 That's one approach. The other is to use similar triangles. You still find the hypotenuse=29 using the pythagorean formula, and then use x/21 = 20/29. Or, (and this leads to the proof I alluded to earlier), you label the left & right parts of the hypotenuse as __a__ & __b__ respectively, and you get x/a = b/x = 20/21, and x/21 = 20/(a+b). I'm not expecting the kids to be able to use that last one. I did, however, expect them to keep looking after they'd already found the answer one way. As far as I can tell, Kate's Trig method reduces to the area solution, since the only given angles (including the included angle of the two given sides) are right angles, and the sine of a right angle is 1. That's one approach.

The other is to use similar triangles.

You still find the hypotenuse=29 using the pythagorean formula, and then use x/21 = 20/29.

Or, (and this leads to the proof I alluded to earlier), you label the left & right parts of the hypotenuse as a & b respectively, and you get x/a = b/x = 20/21, and x/21 = 20/(a+b).

I'm not expecting the kids to be able to use that last one. I did, however, expect them to keep looking after they'd already found the answer one way.

As far as I can tell, Kate's Trig method reduces to the area solution, since the only given angles (including the included angle of the two given sides) are right angles, and the sine of a right angle is 1.

]]> By: Druin http://blog.mathsage.com/?p=538#comment-446 Druin Wed, 11 Feb 2009 00:47:22 +0000 http://blog.mathsage.com/?p=538#comment-446 Okay, I wouldn't use trig at all - isn't that funny how different people solve it differently! I would use the area of the triangle and Pythagorean Theorem. A = 0.5(21x20) = 210 Use Pythagorean Theorem to find the hypotense: 29 And the area formula again.. 210 = 0.5(29)(x) Okay, I wouldn't use trig at all - isn't that funny how different people solve it differently! I would use the area of the triangle and Pythagorean Theorem.

A = 0.5(21×20) = 210

Use Pythagorean Theorem to find the hypotense: 29

And the area formula again..
210 = 0.5(29)(x)

]]> By: Kate http://blog.mathsage.com/?p=538#comment-436 Kate Sun, 08 Feb 2009 15:00:18 +0000 http://blog.mathsage.com/?p=538#comment-436 Geometry kids wouldn't do it, but after a little right triangle trig, you could find the area with .5absinC, and then use the area to find the altitude. Geometry kids wouldn't do it, but after a little right triangle trig, you could find the area with .5absinC, and then use the area to find the altitude.

]]> By: Mr. K http://blog.mathsage.com/?p=538#comment-435 Mr. K Sun, 08 Feb 2009 14:43:05 +0000 http://blog.mathsage.com/?p=538#comment-435 I actually found 3 ways to solve this (so far). The trig kids may jump straight to similar triangles with the pythagorean theorem, which is not actually the easiest way to solve this. I'm thinking that he fact that it can be solved using only similar triangles without the pythagorean theorem leads to a potential proof once you generalize the problem. I'm pretty sure my kids' algebra skills aren't strong enough for that, though. I actually found 3 ways to solve this (so far).

The trig kids may jump straight to similar triangles with the pythagorean theorem, which is not actually the easiest way to solve this.

I'm thinking that he fact that it can be solved using only similar triangles without the pythagorean theorem leads to a potential proof once you generalize the problem.

I'm pretty sure my kids' algebra skills aren't strong enough for that, though.

]]> By: Dan Stucke http://blog.mathsage.com/?p=538#comment-434 Dan Stucke Sun, 08 Feb 2009 10:22:42 +0000 http://blog.mathsage.com/?p=538#comment-434 Is it 14.48? Nice little problem, I have just finished teaching trig & pythagoras with a class of mine and will set them this to warm them up on Monday morning. Is it 14.48?

Nice little problem, I have just finished teaching trig & pythagoras with a class of mine and will set them this to warm them up on Monday morning.

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