maths communication when solving

S

Stevey f

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Dec 16, 2014
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2
Hello All.

I am currently do an open degree in engineering and i am currently still in my first year which contains quite a bit of maths. I am ok when it comes to solving answers but the way i communicate how i show my working is what fails me to maintain high marks. At the moment my average grade is 87% which to be fair is still a good average but i know i am better and i can achieve a better result so when i transfer over to next year higher maths i will have a better standing to try maintain high marks and i would be more happier with myself if i could have an average over 90%

now geometry confuses me. i can solve angles happily but writing down how the book suggests gets me in all sorts of knots and twists

one of the questions (see attached) ask to find <abc in terms of 0 (theta) ((any 0 should be treated as theta, any answer that is 0 i have used Zero to indicate))

Answer (a)

<CBD = 180-30-0 = 150-0
But AD is a straight line, so
<ABC + <CBD = 180 (this is where i start getting confused because with all that added letters)
<ABC = 180 -<CBD
=180-(150-0)
=180-150+0 (why does this suddenley go from being in brackets from a negative to a positive)
=30+0

Answer (b)

Using the fact that the angles in a triangle add up to 180 gives <ABD =180-90-0
Which simplifies too <ABD=90-0

Now <ABC, <ABD and <DBE add to 180 as they are angles on a straight line EC.
Since <DBE is 90 and we have just found that <ABD = 90-0 this gives the equation
<ABC+ (90-0)+90 =180

So <ABC -0 = zero
<ABC = 0

where i struggle with is that the letters dont tie up with the angles because 1 letter is trying to represent many different angles. and i try to find a way where each letter used represents the angles in the same order for example if we had a triange with the apex listed as A being 40 and the two base angles being 70

<ABC = 40+70+70 when i read it A= 40 B=70 C=70

I would appreciate if anyone has any tips on how to read this information and being able to reproduce it for future explanations so i can continue to improve

Thanks
Steve

(apologies if i have confused anyone)
 

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Stevey f said:
...find <abc in terms of 0 (theta) ((any 0 should be treated as theta, any answer that is 0 i have used Zero to indicate))
Click to expand...
Thank you for explaining your notation. However, sometimes (in your scheme) something like "70" could be meant to express "seven times theta" rather than "the number seventy". So another shorthand for "theta" is "@" -- but make sure you define this character if you're using it for "theta".

Stevey f said:
=180-(150-0)
=180-150+0 (why does this suddenley go from being in brackets from a negative to a positive)
Click to expand...
Because that's what happens when you take the "minus" through the parentheses: 180 - (150 - @) = 180 - 1(150 - @) = 150 + (-1)(150 - @) = 150 + (-1)(15) + (-1)(-@) = 150 + (-15) + (+@) = 150 - 15 + @.

Stevey f said:
where i struggle with is that the letters dont tie up with the angles because 1 letter is trying to represent many different angles.
Click to expand...
Then maybe try labelling things. For instance, let <ABC be called \(\displaystyle \alpha,\) <CBD be called \(\displaystyle \beta,\) etc. Just be sure to define the names in your solution. ;)
 
Stevey f said:
Hello All.

I am currently do an open degree in engineering and i am currently still in my first year which contains quite a bit of maths. I am ok when it comes to solving answers but the way i communicate how i show my working is what fails me to maintain high marks. At the moment my average grade is 87% which to be fair is still a good average but i know i am better and i can achieve a better result so when i transfer over to next year higher maths i will have a better standing to try maintain high marks and i would be more happier with myself if i could have an average over 90%

now geometry confuses me. i can solve angles happily but writing down how the book suggests gets me in all sorts of knots and twists

one of the questions (see attached) ask to find <abc in terms of 0 (theta) ((any 0 should be treated as theta, any answer that is 0 i have used Zero to indicate))

Answer (a)

<CBD = 180-30-0 = 150-0
But AD is a straight line, so
<ABC + <CBD = 180 (this is where i start getting confused because with all that added letters)
<ABC = 180 -<CBD
=180-(150-0)
=180-150+0 (why does this suddenley go from being in brackets from a negative to a positive)
=30+0

Answer (b)

Using the fact that the angles in a triangle add up to 180 gives <ABD =180-90-0
Which simplifies too <ABD=90-0

Now <ABC, <ABD and <DBE add to 180 as they are angles on a straight line EC.
Since <DBE is 90 and we have just found that <ABD = 90-0 this gives the equation
<ABC+ (90-0)+90 =180

So <ABC -0 = zero
<ABC = 0

where i struggle with is that the letters dont tie up with the angles because 1 letter is trying to represent many different angles. and i try to find a way where each letter used represents the angles in the same order for example if we had a triange with the apex listed as A being 40 and the two base angles being 70

<ABC = 40+70+70 when i read it A= 40 B=70 C=70

I would appreciate if anyone has any tips on how to read this information and being able to reproduce it for future explanations so i can continue to improve

Thanks
Steve

(apologies if i have confused anyone)
Click to expand...

A lot of times angles are indicated with the three letters which indicate the angle formed by the line segments going from the first letter to the second letter and from the second letter to the third letter. For example, <ABC would mean the angle between line segment AB and line segment BC at B. Sometimes, the angle is written near the intersection of the two line and between them to indicate the angle, like, as stapel suggested, using a single letter to represent that angle. Sometimes, also, a small part of a circle is drawn to indicate the angle like at <ABC in the image.
 
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