Don't hunt me, Chakie. But can you provide a step-by-step workout to determine angle x as shown below, using ONLY elementary geometry, such as the sum of internal angles and other basic properties of a triangle. I remember my math teacher said trigonometry, the law of sines, and the law of cosines are not allowed. And it is not a trick question.

I, frankly do not know the true answer, and I'm not testing you. It is just a look-so-easy geometry problem. I must humbly tell you that I have also worked on it for many hours since yesterday to determine angle x using only elementary geometry. Perhaps, it is time to invite Krevaki, p3nguin, studyboy, & TSOM to unleash the Wisdom of Crowds.

Hi Flame Haze, Intermission, kingkingyyk, maximR

If you have some time, please drop by this thread because I want to borrow your Brilliance to find the angle x!

At first, I was thinking there must be some kind of geometrical properties either so new or unknown to me. But after draining all my grey matter, I finally discovered the following relationship which can be mathematically proven. However, I'm not sure whether I have just rediscovered the work of other scholar, or the theorem has been repeatedly appeared in numerous publications in the past. Anyhow, by applying the following theorem, the angle x can be determined in seconds. Perhaps, you could verify this theorem too. Also thanks ChuckyHuntsYou for provoking me!



The above theorem shall be read in conjunction with the Triangle Problem 1 figure.
Some wordings may need to be refined or rephrased in future for the sake of clarity.
Point 'O' (not shown in figure) is the intersection between Line AE and Line BD.

This post has been edited by Critical_Fallacy: Aug 31 2013, 05:57 AM

There are generally 5 methods that I can think of (up to A-level) to find the shortest distance from a point P(x0, y0) to a line (either Ax + By + C = 0, or y = mx + c).

(1) Formulas [2 formulas: |Ax0 + By0 + C| / √(A² + B²) and |y0 − mx0 − c| / √(m² + 1)]
(2) Geometry [2 techniques: Line equations & Area of a Triangle]
(3) Calculus [involving parametric equation with an additional parameter, t, (time variable) on top of x, y, & z*]
(4) Trigonometry
(5) Vector [2 techniques: Vector projection formula & Magnitude of the Normal Vector]

As with many examples we have seen in mathematics, the method of solution should be assessed in terms of the goodness of the answer in the context of the information available. For instance, sometimes only the coordinates of the points are given. Other times, the line vector and the position vector are provided. I think you got it...

* The z or height parameter occurs only in 3-D space. In planar environment, parameters x & y are suffice, because z is referenced at 0.

But “why is the woman pregnant in the first place?” is the an undirected question that contains multiple answers.

Basically, good nutrition during pregnancy can help to keep your Mum and your developing baby sister healthy. Pregnant women need more protein, iron, folate and iodine but only a small increase in energy (kilojoules). Folic acid supplements before and after conception can reduce the risk of neural tube defects such as spina bifida.

If the question asks to state two permanent birth controls for women, then Tubal ligation and Hysteroscopic sterilization are the specific surgical and non-surgical procedures to induce permanent infertility.

I think you have your own answer to that question from another thread. So what answer would you pose?

But here are some conceivable answers from the medical perspective:

(1) Natural conception
(2) In vitro fertilization (IVF)
(3) Fertilized egg must attach to the lining of the womb
(4) The egg must continue to grow normally from an embryo to a fetus

If natural conception occurs through the unprotected sex with a HUMAN male, then your answer is probably true. NOT definitely true!

This post has been edited by Critical_Fallacy: Sep 2 2013, 10:06 PM