Draw a right triangle with an acute angle and radius of incircle given

Mariele

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Hello, I have the following problems:

1. Draw a right angled triangle of which an acute angle measures 60 degrees and the radius of the incircle is 4
2. Find the sides of this triangle

I found a solution, but my math teacher said my answer is wrong. I really can't see what I've done wrong because when I draw my triangle, everything seems to be correct. I can’t ask him for help because I don’t see him anymore this month. You can find my approach on these problems in the attachment.

Can someone tell me why my method is wrong?
 
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Hello, I have the following problems:

1. Draw a right angled triangle of which an acute angle measures 60 degrees and the radius of the incircle is 4
2. Find the sides of this triangle

I found a solution, but my math teacher said my answer is wrong. I really can't see what I've done wrong because when I draw my triangle, everything seems to be correct. I can’t ask him for help because I don’t see him anymore this month. You can find my approach on these problems in the attachment.

Can someone tell me why my method is wrong?

The picture has too little resolution; but what I can make out from it looks as if you probably have a valid idea. Can you either post a better picture (a screen shot might be all you need), or tell us in words what you did?

Also, do you have any sense whether it is your drawing or your numerical answer, or both, that is being called wrong? Are there any restrictions on how you do the drawing (e.g. a compass and straightedge construction)? Have you quoted the entire assignment word for word?
 
We get better results by uploading three separate (cropped) images instead of combining three full pages into a single, very wide image. Most screens are too narrow to display three adjacent pages legibly, especially after reduction by forum software to fit a portion of the page frame. Zooming doesn't help, either, because your image is low-quality.

:idea: You can use the Preview Post button, to check how submissions will appear, before posting them. This gives you an opportunity to fix issues.
 
The picture has too little resolution; but what I can make out from it looks as if you probably have a valid idea. Can you either post a better picture (a screen shot might be all you need), or tell us in words what you did?

Also, do you have any sense whether it is your drawing or your numerical answer, or both, that is being called wrong? Are there any restrictions on how you do the drawing (e.g. a compass and straightedge construction)? Have you quoted the entire assignment word for word?

I've put the screenshots in the links below:

https://ibb.co/hcrkEm (first picture)
https://ibb.co/cissum (second)
https://ibb.co/nH7QEm (third)

I don't know if my drawing or answer is wrong, because I heard through someone else that my answer was wrong. I only used the compass to draw the circle and a protractor triangle to draw my tangent lines.
 
Ohhh...r = 4, not 42 (the "2" stuck to the "4"
when I quoted your ORIGINAL post!).

Anyhow, same thing:
[a + a*sqrt(3) - 2*a] / 2 = 4

So a = 2r / (sqrt(3)-1)

I don't know why you did all the work you did
when you simply could have used the standard
r = (a + b - c)/2 formula, which means easy/quick
solution since you're using a 30-60-90 triangle.

I didn't know of this formula before handing in the solution to my teacher, so I had to use the longer version. But do you know if my drawing is correct?
 
Also, do you have any sense whether it is your drawing or your numerical answer, or both, that is being called wrong? Are there any restrictions on how you do the drawing (e.g. a compass and straightedge construction)? Have you quoted the entire assignment word for word?

Mariele, you haven't answered my questions along with fixing the pictures. Doing so might help us tell you what, if anything, is "wrong". We can't tell yet what standards to judge your work by.

If you were assigned to do a proper construction, then possibly the issue is that you have not clearly distinguished the actual construction from the thinking that leads to it; I find it hard to follow, when you say you "found a point", then tell us the reasoning behind doing so, and only then tell us what you did, but in somewhat vague language. The fact that you show a lot of grossly rounded numerical values rather than exact values (radicals) is troubling.

I think everything you did may be correct (and perhaps a reasonable way to do the construction); though there are somewhat quicker ways to do it, that would not make it "wrong". Do you think your teacher might have meant that what you did is not properly justified, or explained adequately?
 
Mariele, you haven't answered my questions along with fixing the pictures. Doing so might help us tell you what, if anything, is "wrong". We can't tell yet what standards to judge your work by.

If you were assigned to do a proper construction, then possibly the issue is that you have not clearly distinguished the actual construction from the thinking that leads to it; I find it hard to follow, when you say you "found a point", then tell us the reasoning behind doing so, and only then tell us what you did, but in somewhat vague language. The fact that you show a lot of grossly rounded numerical values rather than exact values (radicals) is troubling.

I think everything you did may be correct (and perhaps a reasonable way to do the construction); though there are somewhat quicker ways to do it, that would not make it "wrong". Do you think your teacher might have meant that what you did is not properly justified, or explained adequately?

My original solution was written in Dutch (becaue I'm from Belgium) so maybe I didn't properly translated it to English. There were some parts that I didn't know how to say mathematically in English, so that could also be a reason why my explanation wasn't very clear. I'll ask my teacher when I see him again, but thank you for your effort!
 
My original solution was written in Dutch (because I'm from Belgium) so maybe I didn't properly translated it to English. There were some parts that I didn't know how to say mathematically in English, so that could also be a reason why my explanation wasn't very clear. I'll ask my teacher when I see him again, but thank you for your effort!

I wasn't saying that the solution isn't explained mathematically, but that you didn't directly tell us what you were assigned to do. As a result, we don't know what your teacher would consider to be a correct answer. In addition, by mixing together the reason for each step with the process, it took me considerable effort to see what you actually did. This is a matter of style, not just of language. The result is that even if you were right, it was not clear; and what you wrote obscured the place where you didn't do what your teacher probably required, namely to make an exact construction.

Here is my understanding of what you did, stated in such a way that it is clear how you constructed the triangle:

I constructed a circle with radius 4 and extended a radius, M1M2, the same distance beyond the circumference to A. Then I constructed tangents to the circle, AP1 and AP2, so that angle P1AP2 is 60°, since AM1P1 and AM1P2 are 30-60-90 triangles. (I presume you have learned how to do this, so you don't need to state the details.)

Then I extended line AP1, and intersected it with a circle centered at M1 so that BM1 = 4/sin(15°) = 15.5, and M1BP1 = 15°. [This is probably what your teacher objects to, because a proper construction does not use calculated measurements; the correct value for BM1 is 15.454813..., not 15.5, so you can't construct it exactly without further work.]

Then I constructed a chord P1P3 perpendicular to BM1, so that BP3 is tangent to the circle.

Finally, I extended tangents BP3 and AP2 to meet at C. Triangle ABC meets the requirements.

One way to make this a proper construction is to first construct tangent AP2 and radius M1P3 parallel to AP2. Then make tangent line BC perpendicular to M1P3. This ensures that BCA is a right angle and the circle is tangent to the sides.

You would want to state the proof that each step does what you want, after showing the construction.
 
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