Kathryn Posted February 13, 2017 Share Posted February 13, 2017 Singapore Standard 6B problem. The total angle HAY is 105 degrees. It's made of two smaller angles: HAS and SAY. Angle HAS is 10% greater than angle SAY. Find angle HAS. I cannot figure out how to do this without algebra. Help! Quote Link to comment Share on other sites More sharing options...
73349 Posted February 13, 2017 Share Posted February 13, 2017 I'd start with finding out what they'd be if they were equal (half of 105) first and adjust from there. I don't have SM 6, though, to know if that's how the book is looking to have you do it. Quote Link to comment Share on other sites More sharing options...
Monica_in_Switzerland Posted February 13, 2017 Share Posted February 13, 2017 (edited) Did you make a bar model? I'd probably make a model that looks initially like: (---------------105-----------) (------X-----)(-----X-----)(-.1X-) Then I'd change it all to a new variable equal to .1X, so the bottom bar would become: (------10Y-----)(-----10Y-----)(--Y--) From there, you would do: 105 / 21 = 5 Angle SAY = 10 Y = 50° Angle HAS = 11Y =55° ETA: I'm using the word variable here- I think it's been introduced already in 6, but if not, it's more about intuition once you see the bar model that you need 21 pieces in total. Edited February 13, 2017 by Monica_in_Switzerland Quote Link to comment Share on other sites More sharing options...
Kathryn Posted February 13, 2017 Author Share Posted February 13, 2017 Did you make a bar model? I'd probably make a model that looks initially like: (---------------105-----------) (------X-----)(-----X-----)(-.1X-) Then I'd change it all to a new variable equal to .1X, so the bottom bar would become: (------10Y-----)(-----10Y-----)(--Y--) From there, you would do: 105 / 21 = 5 Angle SAY = 10 Y = 50° Angle HAS = 11Y =55° ETA: I'm using the word variable here- I think it's been introduced already in 6, but if not, it's more about intuition once you see the bar model that you need 21 pieces in total. Thank you! This works. I could only think of making two equations A+B=105 A=1.1B And then solving from there. 1 Quote Link to comment Share on other sites More sharing options...
ondreeuh Posted February 13, 2017 Share Posted February 13, 2017 I would look at it this way: the first angle is 100% of its value, and the second angle is 110% of the first angle. The GCF of 100 and 110 is 10, so I would split divide both angles by 10, so the first angle will have 10 parts and the second angle will have 11 (each worth 10%). Now all 21 parts equal 105 degrees, so divide 105 by 21 and you get 5 degrees. So each 10% is worth 5 degrees. HAS is 10x5 and SAY is 11x5 (55). Quote Link to comment Share on other sites More sharing options...
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