5

5 . In this question angles are measured in degrees. A triangle T has one side of length 1 and another side of length 2 with the included angle between them of size...

Question

5 . In this question angles are measured in degrees. A triangle T has one side of length 1 and another side of length 2 with the included angle between them of size 458_ (a) Calculate the length of the remaining side of T:

5 . In this question angles are measured in degrees. A triangle T has one side of length 1 and another side of length 2 with the included angle between them of size 458_ (a) Calculate the length of the remaining side of T:



Answers

Given: $\overline{A S} \| \overline{B T};$
$$m \angle 4=m \angle 5:$$
$$\overrightarrow{S B} \text { bisects } \angle A S T$$
Find the measure of $\angle 1$ .

All right, or this problem. You're given a right triangle where C is the right angle and we know that the measurement of angle is less than the measurement of Angle B, and we know that the side links our two times Square 252 and four. So to begin, let's look at the how partners the hot pot news is. Always decide ling opposite the right angle, and it is always the longest silence of the triangle. So are three. Given silence are to square 252 and four and the largest of which will be to square 25 So the hot pot new slink is two times square to five because it is the longest of the three side links, and we know that the measurement of angle A is less than the measurement of angle B. And since this is the case, the saddling opposite angle a must be less than the side length opposite Angle B, so they could be said that a must be less than be. And since our two remaining silent star two and four, that would mean that this settling must be two in this one must be for Now we're asking Santa Fe the coast under way and the tangent of a now using the new Monix socket toe, the son of the angle A which is drawn right here. Does it go to the opposite side of length? About about the link? What news? The opposite side length is, too. And the length of the hot partners is too scared of fun. So we're gonna have to devote about two square to five for the sign of a and the coast on of a single to the adjacent side length divided by the length of a hot partners. And that is going to be equal to four. Have you thought about to square 25? And the tangent of a Tanja today is going to be able to the opposite side length, divided by the adjacent silent clinches, too. What about four? Now, these can be further simplified. Um, using rationalization. Um, but these are our correct answers.

Okay, so here we're going to have a right triangle and the hard part news is five and one of the legs is too, and we want to sold for the angle. So let's call this angle A in this angle, be OK, So let's someone angle a, um for angle A you see that we have the opposite side in the high pot. New. So we're gonna be doing sign. It's a sign of angle. A is going to be equal to the opposite to and over the high partners we just bought. So because we're trying to find the angle, we are going to be using the ember sign off to over five plus a little calculator and we get that angle A is 23.58 degrees. Okay, now we do the same thing for angle B, but for end will be. We have the sides adjacent, and the head partners we're gonna be using co sign so co sign off Angle B is equal to adjacent overheard Got news. Take the inverse co sign. Then we get that, um, angle B is 66.42 degrees, and that's your answer

Mhm. All right. So, this question here was asking about the measure of angles in a triangle. I've labelled a picture here with the angles A. B and C. They tell us everything in terms of A. So from an algebra standpoint, we should be writing in terms of the variable A. The measure of angle B is five times A. A. Is just going to stay itself. And they told us in the question at sea is the measure of a minus two degrees. So we should know putting all this information here together that the sum of all these angles here should be 180 degrees in a triangle. So we have A plus B. Now be is really five A in this case plus C, which is a minus two. It's all equal to 180 degrees. This is a nice easy one step equation here. So I'm just going to combine like terms C. Seven A minus two people to 1 80 Universe operations add to to both sides. Seven A is equal to 1 82 right by seven. So if you do that on your calculator, 1 80 two, divided by seven, you should get about 26. So filling out the rest of these, we now know that A. Is 26 degrees B is gonna be five times 26 which should be 130 and C is 26 minus two, which is 24 degrees. Okay?

We're told that we have a right triangle. And I'm just gonna make kind of a generic right triangle. I'm not going to try to proportionate out. And we have sides of 3 36 5 27 and 6 25. And so 6 25 would have to be the high pot news. 3 36 could be a leg and we don't know which leg. And let's call this angle A. And this angle be. So when we're dealing with this, you can use pythagorean theorem to verify that 3 36 squared plus 5 27 squared is equal to 625 square at least approximately. So, So if we want to find angle a let's use for angle a uh we can use a tangent function. We can use the coastline function. We can use a sine function but we have to use the trig function. Let's use tangent tangent of angle a is equal to opposite which is 527 Over adjacent. Which is this? 336. And if we take the Inverse Tan, the Inverse Tan of that ratio will give us the appropriate angle. And we want to have our calculator in degree mode which from the previous question I had it in radiant road. So I definitely have to change it. And so are inverse tan of 5 27 divided by 3 36 gives us an angle of 57.48°. And I believe your directions tell you to give a grounded to a to place decimal. Now we could go through and use just accomplished the compliment to find this angle be. But instead let's use the trade function. Oh and let's just be wild. And let's use the cosine function co sign of angle B is equal to and let's go adjacent, which is 5 27 Over hypotenuse which is 6:25. And so when we find the inverse co sign of that ratio. Yeah. Oh so in verse co signing my calculator is in excuse me. In degree mode 5 27 divided by 6 25. We should get an angle that's complementary to that. So when we do that we get 32.52 degrees. And notice that when I add these two angles together they do add up to 90 degrees. So those are our two acute angles.


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