Weird Triangle

[ekko20six]

Ok all, i have a maths question for you which all the details are attached in the picture...

basically you work the area of a triangle and get area a then you work out the areas of the shapes inside (4 small triangles and one rectangle) and instead of getting area a you get area b.

why do you get different answers?

[monkey13]

Because the overall shape isn't a triangle.

If we calculate the angle of B between the hypotenuse and the base ( x = tan^-1(5/3)) we get 59.03. The angle of C between the base and the hypotenuse should be the same. ( x = tan^-1(8/5)) but it isn't its 57.99. So it's not a triangle. This is confirmed if we try to calculate the angle in triangle B using the whole shape height and half the base. ( x = tan^-1(13/8)) We get 58.39.

They should all get the same angle so it's not a triangle.

[xendrome]

^Pwned.....

[Keito]

Because the overall shape isn't a triangle.

If we calculate the angle of B between the hypotenuse and the base ( x = tan^-1(5/3)) we get 59.03. The angle of C between the base and the hypotenuse should be the same. ( x = tan^-1(8/5)) but it isn't its 57.99. So it's not a triangle. This is confirmed if we try to calculate the angle in triangle B using the whole shape height and half the base. ( x = tan^-1(13/8)) We get 58.39.

They should all get the same angle so it's not a triangle.

ehhrm, I'm certain your math is correct and all, but isn't a triangle just like... something with three corners? Non-native english speaker here, I was in the perception that a triangle is antyhing with 3 corners :p sort of like a rectangle having 4 and such (and a square having to be square...yet still a rectangle)

[monkey13]

Yeah a triangle is something with three corners but this shape has five.

Top, bottom left, bottom right, where the top of B meets the bottom left of C and where the top of E meets the bottom right of E.

It's only a one degree change in angle which makes the top of this shape larger than it should be if it was a triangle hence the differences in areas.

[Eoin]

You are correct that anything with three corners is a triangle, but Keito's point is that the shape actually has 5 corners, two are just too subtle to see in the image shown.

edit- beaten to it :)

[Keito]

Need to change the names Eoin ;) but I get it :)

[MillionVoltss]

good idea for a topic, really hard question or problem or what am I then next person ha to answer and put there question in.

[monkey13]

Now come on jasperau. Do I not get any kind of confirmation that I'm right? Maybe I'm not? No acknowledgement or thanks? Either I helped you with something or you were trying to stump everyone and didn't. Which was it?

[+Nik Louch Subscriber²]

I'm over-emphasizing it here to show - but this is not a triangle.

[ekko20six]

Now come on jasperau. Do I not get any kind of confirmation that I'm right? Maybe I'm not? No acknowledgement or thanks? Either I helped you with something or you were trying to stump everyone and didn't. Which was it?

lol sorry there,

i forgot to come back and comment.

well the thing is, this is a question for year 8 maths in western OZ, so they have not learnt how to use SIN, COS or TAN yet...

i get what ur saying with the 'its not a real triangle' but i am wondering if there is a simpler explanation???

any thoughts...?

[monkey13]

Ah ok is that about 13-14 years old? I thought I'd learnt some trigonometric functions by then but maybe it was a bit later.

Anyway you can do it another way. Triangles B and C should have all the same internal angles. So they are just different sizes of the same triangle. Taking the difference between the heights of B and C (8/5) C is 1.6 times higher than B. If B was just a smaller version of C then the base of C (5) would be 1.6 times the base of B(3) but it isn't. (3*1.6 = 4.8). So they don't have the same internal angles so overall it's not a triangle.