As we found out, the study of geometry is primarily related to the search for missing measurements, both the length of the sides and the angular measurements, in geometric figures. If a shape has four or more sides, we often divide the shape into triangles, drawing diagonals, heights, median and / or angular bisectors. The reason for this division into triangles is that we have several labels for finding missing dimensions in certain triangles.
We have already considered 30-60 right and 45-right "special" triangles. (They are sometimes called 30-60-90 and 45-45-90 special triangles.) These right triangles have relationships or relationships for three sides, which are always the same, and we can use these well-known relations to reduce the work needed to find the missing side measurements . These special triangles are certainly useful, but they only work with two types of regular triangles. How about all the other regular triangles? To work with all these right triangles, we use the relationship SOHCAHTOA - pronounced shi-ka-toa.
I know that this word sounds like it might be an American Indian word, but this is really a mnemonic device for memorizing the relationship of the sides and angles in the right triangle. To understand everything in this mnemonic device, we need to learn some new terms. These terms are crucial to success in both geometry and trigonometry, so it is important to get solid information about this information. You will not stop using it at the end of Geometry.
The letters in SOHCAHTOA mean that from left to right, S ine, ABOUT pposite HOUR ypotenuse, FROM osine, djacent HOUR ypotenuse, T angent, ABOUT pposite and djacent. At this point in your studies, the words sine, cosine, and tangent may seem familiar to you from your graphical or scientific calculators, although calculators use the abbreviations sin, cos, and tan; but these words probably have no meaning to you. This is normal and good.
Triangles have three sides, so there are six ways in which we could compare the two sides together, if we correctly understand that the opposite of each other. The six ways to compare two sides together form six trigonometric relationships. Sine, cosine and tangent are the three most commonly used of the six trigger factors. As you remember, a relationship is just a comparison of two numbers. Attitude can be written in the form of decimal fractions, fractions and cents. To work with right triangles, we compare the numbers of two sides of a triangle.
To fully understand the SOHCAHTOA, we need a diagram. On a piece of paper - the one that you have on hand while reading maths articles - draw a reverse capital letter "L.". Make your legs noticeably different in length. Now draw a line segment connecting the far end points of the legs. Mark the lower left corner of the letter A outside, but close to the corner. Name the upper corner as B and name the angle of 90 degrees as C. Now we need to designate the sides as addends, adjacent, opposite and hypotenuse. The hypotenuse is always the opposite side of the right angle, but the other two labels are “relative”. This means that they are different if we consider angle a and not angle B. For example, in our triangle, the opposite angle B is the AC segment, but the opposite angle A is the BC segment. Thus, marking is not possible until we know which corner to use.
We are almost ready to explain what constitutes SOHCAHTOA, but there is one point that I want to emphasize, which is overlooked by most of the students of Geometry. When we write in the short version sin = opp / hyp, we leave a very important part of the statement. This relationship depends on the angle used. The short version sin = opp / hyp means a longer sentence, “The ratio of sines for a given angle X is the ratio of the side opposite to X to the hypotenuse of a triangle. You should always remember that the words sin, cos and tan should be read by sine of A or cosine from B or tangent from X. NEVER FORGET UGOV!
Using X to designate an angle, SOHCAHTOA denotes the following relationships: sine x = opposite / hypotenuse, cosine X = contiguous / hypotenuse, and tangent X = opposite / contiguous. They are often written in short form: sin = opp / hyp, cos = adj / hyp and tan = opp / adj.
In another article, we will look at how to actually use the SOHCAHTOA to find the missing sides and corners, but as a quick check of what we have just discussed here, let us use some specific sides. Let us use the right triangle 3, 4, 5 and the picture we drew earlier. Designate the hypotenuse with 5, the base with 3, and the vertical with 4, and we will use the names of the angles A and B and C earlier. Using these numbers, sin A = 4/5, cos A = 3/5 and tan A = 4/3. If you agree with these figures, you understand this material well. If these numbers do not make sense yet, reread this article and re-draw the chart as many times as necessary to make this relationship clear.
In the following articles we will give meaning and purpose to the process that we introduce. At the moment it is important to remember that trigger functions are nothing more than the ratio of the two sides of the right triangle. In another article, we will use these factors to find the missing angle, and in another article we will look at how to give these visual images a meaning in your head, so that you can evaluate the answers. We will always have calculators and computers to do the hard work for us; but often we just need to have a quick ball assessment. We can also learn this skill.
SOHCAHTOA is a very powerful tool - the one you want to master as quickly as possible. In addition, it makes you seem REALLY SMART !!!!!! That alone is worth it!
