# Geometry's a challenge

Ramned
Posers and Puzzles 22 Jun '07 12:18
1. Ramned
The Rams
22 Jun '07 12:18
Are you a geometrical thinker by chance? I am going to make some questions similar to the physics one. Starting easy.

1. What does pi round to in the nearest hundreth?
2. What is the x intercept of the equation, y = 3x - 3?
3. If you had a circle in space, and plotted points 3 points equidistant from the center of that circle, describe the form that the points create, as specifically as you can.
4. What do you get if you take tangent of the right angle of a triangle?
5. How would you find the distance between A(0,-3) and B(4,4) ?

I can take this much further than the Physics one, so let's see if there are geometry geniuses
2. PBE6
Bananarama
22 Jun '07 14:37
Originally posted by Ramned
Are you a geometrical thinker by chance? I am going to make some questions similar to the physics one. Starting easy.

1. What does pi round to in the nearest hundreth?
2. What is the x intercept of the equation, y = 3x - 3?
3. If you had a circle in space, and plotted points 3 points equidistant from the center of that circle, describe the form that the ...[text shortened]...
I can take this much further than the Physics one, so let's see if there are geometry geniuses
1. 3.14
2. When y=0, x=1. This is the x-intercept.
3. A triangle.
4. A headache! The tangent of 90 degrees is undefined. It approaches +inf as you approach 90 degrees from the left, and -inf as you approach from the right.
5. Use the Pythagoream theorem. D^2 = (x2-x1)^2 + (y2-y1)^2. In this case it happens to be sqrt(65).
3. 23 Jun '07 06:37
Originally posted by Ramned
Are you a geometrical thinker by chance? I am going to make some questions similar to the physics one. Starting easy.

1. What does pi round to in the nearest hundreth?
2. What is the x intercept of the equation, y = 3x - 3?
3. If you had a circle in space, and plotted points 3 points equidistant from the center of that circle, describe the form that the ...[text shortened]...
I can take this much further than the Physics one, so let's see if there are geometry geniuses
1. 3.14
2. P (1,0)
3. Triangle, I think, at least 2 angles have to be equal (sorry, no proof, just intuition)
4. Limit at a point that has 2 slopes at 1 time is undefined.
5. D=(16+49)^(1/2)=65^.5

Anything harder maybe next time?
4. Ramned
The Rams
23 Jun '07 12:041 edit
Number 3 was tricky. It is in space. Therefore if you plot 3 points from the center of the circle, you go up 3, down 3, right 3, left 3, diagnol 3....a sphere with a radius of 3 and diameter of 6. Took some thought.

1. If you had a line on a plane, and plotted points equidistant from the line, describe the condition you'd meet.
2. What is the easiest way to find the sum of the interior angles of a 50 sided figure?
3. What is the measure of 1 exterior angle of a dodecagon?
4. In a 90 degree triangle, ABC, side A is the short leg, B the long leg, and C the hypotenuse. One of the other angles = 30 degrees. Leg A = 5 cm. Find length of the hypotenuse, without using sin/cos/tan.

Those are a decent step up. Harder to come once you get these correct
5. 23 Jun '07 12:26
Originally posted by Citizen John
3. Triangle, I think, at least 2 angles have to be equal (sorry, no proof, just intuition)
They don't have to have 2 angles the same, because you can create any right triangle, where the hypotenuse is the diameter of the circle.
6. 23 Jun '07 12:30
Originally posted by Ramned
4. What do you get if you take tangent of the right angle of a triangle?
Cannot take the tangent of the right angle, because the definition of tangent of an angle is the ratio of the length of the opposite side of a theoretical triangle over the length of the adjacent side of the same triangle. When trying to calculate the ratio, it is impossible to create the triangle as such. The comments by PBE6 and Citizen John are correct as well using the graph. However, it is also impossible to calculate the sin and cos using the 90 degree angle in a right triangle because the sides are not defined (what is adjacent and what is opposite?) even thought the sin and cos of 90 degrees is a value. In these cases you would have to use sin law or cosine law to complete your math.
7. 23 Jun '07 12:302 edits
Originally posted by Ramned
Number 3 was tricky. It is in space. Therefore if you plot 3 points from the center of the circle, you go up 3, down 3, right 3, left 3, diagnol 3....a sphere with a radius of 3 and diameter of 6. Took some thought.

1. If you had a line on a plane, and plotted points equidistant from the line, describe the condition you'd meet.
2. What is the easiest way ...[text shortened]... out using sin/cos/tan.

Those are a decent step up. Harder to come once you get these correct
1.I'd get two parallel lines without the given one.
2.Sum of interior angles = 180 * (n - 2) where n is the number of angles. so here we get 180 * 48 = 8640 degrees.
3.Use the formula from previous answer and subtract the result from 360 degrees => 360 - [180 * (12 -2)]/12 = 210 degrees.
4.As leg A is opposite to 30 degree angle, than it is a half of the hypotenuse => C=10 cm. But this actually is usage of sin function. sin30=0.5. I have no idea how in any other way you could get C.
8. 23 Jun '07 12:37
Originally posted by Ramned
1. If you had a line on a plane, and plotted points equidistant from the line, describe the condition you'd meet.
2. What is the easiest way to find the sum of the interior angles of a 50 sided figure?
3. What is the measure of 1 exterior angle of a dodecagon?
4. In a 90 degree triangle, ABC, side A is the short leg, B the long leg, and C the hypotenuse. O ...[text shortened]... out using sin/cos/tan.

Those are a decent step up. Harder to come once you get these correct
1. Three parallel and distinct lines. (the original plus two more)
2. Use the formula (n-2)*180 where n is the number of sides. Therefore, 48*180 = 8640 degrees.
3. A = 360 - (10*180/12) = 210 degrees
4. I don't know what you mean without using sin / cos / tan as any ratios used would in essence be using sin / cos or tan. In this case, the ratio of opposite and hypotenuse is 0.5, and Leg A must be the opposite side as the shortest side is opposite the smallest angle (and the other angles are 90 and 60 from your question), so the hypotenuse is 10 cm. (Glad you used metric.) I can't think of another way of doing this. If there is another solution I would be excited to hear.
9. 23 Jun '07 12:38
Originally posted by Gastel
1. Three parallel and distinct lines. (the original plus two more)
Actually, I screwed up. After reading kbauman's answer (which is almost the same as mine).

There is another solution for 1 and that is an infinite number of parallel and coincident lines.
10. 23 Jun '07 13:07
Originally posted by Ramned
Number 3 was tricky. It is in space. Therefore if you plot 3 points from the center of the circle, you go up 3, down 3, right 3, left 3, diagnol 3....a sphere with a radius of 3 and diameter of 6. Took some thought.

1. If you had a line on a plane, and plotted points equidistant from the line, describe the condition you'd meet.
2. What is the easiest way ...[text shortened]... out using sin/cos/tan.

Those are a decent step up. Harder to come once you get these correct
1) Hollow Cylinder of infinite length. The radius would be equal to the chosen distance.

2) Make 48 Triangles by connecting points, making sure the triangles are on the inside of the figure. The sum of the interior angles is the sum of the angles of the 48 triangles or 48*180 degrees total (8640 degrees)

3) 150 degrees (formula is 180 - 360/# of sides)

4) Make an triangle by mirroring the triangle along the long leg. You now have an equilateral triangle, and since the hypotenuse is one side, and the short leg is half aside, the hypotenuse must be twice the short leg, or 10 cm.
11. 23 Jun '07 21:12
Originally posted by geepamoogle
1) Hollow Cylinder of infinite length. The radius would be equal to the chosen distance.

2) Make 48 Triangles by connecting points, making sure the triangles are on the inside of the figure. The sum of the interior angles is the sum of the angles of the 48 triangles or 48*180 degrees total (8640 degrees)

3) 150 degrees (formula is 180 - 360/# of ...[text shortened]... one side, and the short leg is half aside, the hypotenuse must be twice the short leg, or 10 cm.
1) No. The line is on a plane, a cylinder exists in space.
3) The question is for the exterior angle.
4) Nice.
12. Ramned
The Rams
25 Jun '07 11:28
Cool. Seems though that people don't know 30/60/90 or 45/45/90 triangle rules.

In the 30/60/90, the hypo is 2 times the small leg. The long leg is radical(3) the short.

In 45/45/90, the short = long leg, and the hypo is radical(2) the short or long leg.
13. 25 Jun '07 14:26
Originally posted by Ramned
Cool. Seems though that people don't know 30/60/90 or 45/45/90 triangle rules.

In the 30/60/90, the hypo is 2 times the small leg. The long leg is radical(3) the short.
I'm not sure people didn't know this. Rather, they interpreted it to be an application of sin/cos/tan (which it is - it's a consequence of sin(30) = 0.5), which was disallowed by the question.
14. 25 Jun '07 21:05
Originally posted by mtthw
I'm not sure people didn't know this. Rather, they interpreted it to be an application of sin/cos/tan (which it is - it's a consequence of sin(30) = 0.5), which was disallowed by the question.
15. AThousandYoung