TheApprentice Posted March 17, 2011 Share Posted March 17, 2011 Here is the question my son had difficulty with: With a right triangle C, what are the acute angles? Sine A = 3/5, sine B = 4/5 Sin A = 0.6; sin neg. 1(inverse) is approximately 37 degrees He is having a difficult time figuring out how .6 is approx. 37 degrees. Can anyone help with how this leap is made? I'm not even sure I explained this correctly.:confused: This is lesson 10.22 - 10.25 in Kinetic Books, if anyone is using this. Quote Link to comment Share on other sites More sharing options...
creekland Posted March 17, 2011 Share Posted March 17, 2011 Sine, cosine and tangent are all ratios of sides of a right triangle. When you have sin A = 3/5 it means in a right triangle, the side opposite the angle is 3 and the hypotenuse is 5 or similar ratios that are simplified to these. Any time you have these ratios, angle A has to be 37 degrees (rounded). It doesn't matter if the side opposite A is 30 and the hypotenuse is 50, angle A will be 37 degrees. 0.6 does not equal 37, but a triangle with a ratio of opp/hyp sides of .6 will always have a 37 degree angle. When you have cosine you are using the ratio of the adjacent side (touching side that is not the hypotenuse) to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. Knowing these ratios and angles is very important to many of the disciplines that use math. Does that help? Quote Link to comment Share on other sites More sharing options...
AK_Mom4 Posted March 17, 2011 Share Posted March 17, 2011 Sine, cosine and tangent are all ratios of sides of a right triangle. When you have sin A = 3/5 it means in a right triangle, the side opposite the angle is 3 and the hypotenuse is 5 or similar ratios that are simplified to these. Any time you have these ratios, angle A has to be 37 degrees (rounded). It doesn't matter if the side opposite A is 30 and the hypotenuse is 50, angle A will be 37 degrees. 0.6 does not equal 37, but a triangle with a ratio of opp/hyp sides of .6 will always have a 37 degree angle. When you have cosine you are using the ratio of the adjacent side (touching side that is not the hypotenuse) to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. Knowing these ratios and angles is very important to many of the disciplines that use math. Does that help? That was a really good explanation! My DS15 looked over my shoulder at it and said "They need to go study Chief Soh Cah Toa!" (that's the mnemonic we learned for remembering these ratios) Quote Link to comment Share on other sites More sharing options...
creekland Posted March 17, 2011 Share Posted March 17, 2011 That was a really good explanation! My DS15 looked over my shoulder at it and said "They need to go study Chief Soh Cah Toa!" (that's the mnemonic we learned for remembering these ratios) Our school doesn't teach Soh Cah Toa, but I always inform my classes about him anyway as I feel he is worthwhile. I also taught my 9th grader it last week when they had progressed through right triangles. However, I always do it AFTER they realize these are ratios of the sides, then it's just an easy way to remember the specifics. Some schools teach it without teaching WHAT sine, cosine and tangent are. That's not good IMO. Math without concepts is just memorization - not math. Quote Link to comment Share on other sites More sharing options...
TheApprentice Posted March 17, 2011 Author Share Posted March 17, 2011 Thanks for the help. The lesson taught my son Sah Coh Toa, and he understands how to get the ratios. He was having a difficult time seeing how the ratio = 37 degrees. He wasn't able to make that connection. It looks like it is just something he needs to know/memorize. Signed, Still a bit confused.:( Quote Link to comment Share on other sites More sharing options...
Perry Posted March 17, 2011 Share Posted March 17, 2011 Thanks for the help. The lesson taught my son Sah Coh Toa, and he understands how to get the ratios. He was having a difficult time seeing how the ratio = 37 degrees. He wasn't able to make that connection. It looks like it is just something he needs to know/memorize. Signed, Still a bit confused.:( Does this help? Look at 37 degrees; the value is .6018. It's always going to be .6018. The value of sin A can be looked up in a table or found with a calculator. Same with all the other trig functions. Quote Link to comment Share on other sites More sharing options...
creekland Posted March 17, 2011 Share Posted March 17, 2011 Thanks for the help. The lesson taught my son Sah Coh Toa, and he understands how to get the ratios. He was having a difficult time seeing how the ratio = 37 degrees. He wasn't able to make that connection. It looks like it is just something he needs to know/memorize. Signed, Still a bit confused.:( This is something he will need a calculator or tables for, though some common ones are better to memorize. The tables were created for a quick look up long before there were calculators. The deal is the ratios always lead to the same angle, so if one knows the sides, they know the angle without having to measure it. If one knows a side and the angle, they can figure out the other side(s) without having to measure. This can be important for hard to measure items or when making plans for construction of any sort of thing. Quote Link to comment Share on other sites More sharing options...
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