Hi everyone, good, afternoon, Professor Edna is here, and I'm going to ask you a basic trigonometry, question. Well, determine the acute angles of a capex right triangle that measure a radius of 3 and 1 easy right? Triangle to start with is the one that has an angle that is right and legs are these smaller sides that are glued here at the angle of 90, so I put here the radius of three being this, my leg and 1 being this. The small leg, your contract with my drawing of 3 is more than one it's.
Good it's. Worth it? Well.
So what the question is, determine the acute angles, that is, you want to know who is here called x, and who are they going to call here? Y? Ok, for me to do that. There is a faster way to do it, which is with the tangent one since I, don't have Portuguese impotence, There are two options or it's. The tangent use era because the tangent formula is the opposite side on which the theta already feels that is what I have from the legs, and then I can find it, or I find hypotenuse through from. The Pythagorean theorem, and then I apply cnn.com, sit, but I'll, do it faster?
So I'll use tangent. Ok? So first I'll go on the tangent DX.
The formula for the tangent of an acute angle is the opposite side of the theta of g7, which is just remembered Coca-Cola coca. So who is my side opposite to to side, opposite to x 3 radius and on my side of acceptance, who is devil of seats that the tit already felt the one who is glued to the head already feels the x is a then tangent DX equals root. 3 ok, I can find. The angle that has a tangent equal to the root of three touches. And in this case here is 60 large already say, how do I think I'll give the answer here before the angle, whose tangent radius of three for a triangle is 60 degrees.
It is there, therefore, that at 60 the other angle will have to be 30, right? Because it is already 90 plus 60 150 as the three angles of a triangle, measure 180, the remainder 30, but I will use a new tangent for reach that 30. Ok. So now I'm going to do t agent of y tangent of.
Y will be the same thing, opposite side to y that. Now the y is here look, who is the side opposite to it one on the side of a 180 I already felt that little root of three glue. So already there o 1 over three limb radii that I have to rationalize when a root is at the bottom of the denominator, and how do I do that multiplies the error and exactly by the root that the denominator was on top and bottom. So as not to change my fraction, so I'll have q, tangent of y is equal the one time radius of three.
Radii of 3 over ray of three times dropped from 3 is radius of nine and is three. So at the tangent of my angle, y is root 3 over three. And what angle has this tangent radius of 3 over three is 30 degrees, ok, but as you know this helps, but did you know that the radius from 30 to 60 and radius from 3 over three to 30. And there is a basic table between the name would have good. So how do we go?
How do I know that 60 have we go d3 and 30 have so many people dropped from 3 over three good tabs, basic line. Normally, every teacher teaches this table, we put it as cosine tangent and 30, 45 and 60, which are the notable years. The most important angles of trigonometry are let's say, they are the basis for the rest of the numbers after whoever has a shred of doubt in this has a 10-minute video, showing how I thought the value of the scene and getting to know the main years watching there. Well, how do we make this table being that? The center has people 30 and 45 and 60 thinking scenic in first we put it like.
This look 12 332. One everybody over two everybody with square root in the denominator I'm just not going to put it in the square root at 1 because the lawyer of one is the same, so I don't need it. So I have here. The scene value of 31 half a cosine value of 30 radii of 3 over two is the value of one hundred and forty-five reais of 2 over 2. And so on until people, the tangent rule like this 313 puts square root on these here of -1 by the again, by the square root of 1 and 30 degrees, put 13 weapons. From where I took this here, I'm going to be decorating this one that I'm going to have to decorate, there will be a solution only that the tangent it is in addition to being the opposite side on Capet.
The ascent. It is also the senate divided by the council. So for example, here at the tangent of 45, we took the square root of 2 2, / square root of 2002 as it is the same value o.
It gave a wind tangent of 60. For example, we take the piano square root of 3 over 2, / consed in the middle division of. Infraction repeats the first multiplies by the inverse of the second radius of 32 divides, everything sometimes 12 can cancel to be just root 3 over one, which is to come out of three also here, an angle that the tangent radius of 3 at 60 degrees it's, the same it's, 30 with the difference that it's going to be a root in the denominator I'm going to have to rationalize like I did here, but it's going to be exactly 1 over radii of 3 so that's it folks.
So who are the two acute angles? S of my triangle, 60. Degrees x and 30 degrees o, y. If you want more questions like this, you want to know more details about this table. Anyway, everything you need can put it here as soon as possible. I'll, make sure to answer, ok, a hug Czechoslovakia.