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Szmpk cf0 = 4 sues is sekeried ficn populaton uith confiocncc mtcnal ft O14=vzrince of42Which equzion conectly JEgeaEclcnc2542)0984) 233584) 638(4)...

Question

Szmpk cf0 = 4 sues is sekeried ficn populaton uith confiocncc mtcnal ft O14=vzrince of42Which equzion conectly JEgeaEclcnc2542)0984) 233584) 638(4)

szmpk cf0 = 4 sues is sekeried ficn populaton uith confiocncc mtcnal ft O14= vzrince of42 Which equzion conectly JEgea Eclcnc 2542) 0984) 233584) 638(4)



Answers

$$B=42.88^{\circ}, C=102.40^{\circ}, b=3974 \mathrm{ft}$$

I can't solve this triangle. Since we're given to angles we know that there's only gonna be one solution. We could do 1 80 minus the two given angles to give us angle see. So angle c. 57.36°. And let's set up the law of sines to find one of our missing sides. So I'm gonna do side a. Which is 12.7 over angle a sign of 68.41 Equals we need side be over a sign of Angle B 54.23. So if we cross multiply be will be these two multiplied together Divided by the sine of 68 4 wine. Make sure your calculator is in degree mode. Okay, that gives us 11 08. So we'll go 11 1 for side B mm. And then we'll do another law of sines for side see So I'm going to stay with my 12.7 over the sign of 68.41. Equal sides. See over sign of Angle c. 57.36 and sides. He will be these two multiplied together. Well that's a seven And divided by the sine of 68 41. That gives us 11.50 per side. See so we'll go with 11.5 and your triangle us off

We can start by finding angle a. By using the 180 fact that is the fact that every triangle has 180° in it. And we'll take 1 80 minus the 40 to 88 -10240. And that'll leave us in A. With 34 72 degrees. And it was sort of a lot of signs. So since we have side B. And angle B. Let's do side B over. The sign of angle be equal. Will do most sides see over the sign of Anglesey. So C. Is going to equal these two multiplied together. Yeah. Yeah. And divide by then the sign of the 40- 88. Make sure your calculator is in degree mode. And for c. then we get 5,703.88 so go .89 ft. And we also have to find side A. So let's keep our 3974 over sign of 42.88 Equals A. over the sign of Angle A. 34.72 A. Will equal these two multiplied together. Mhm. And then divide by a sign of 42.88. Yeah. And for angle a. Then we have 3,326.33. So we'll go .3 and your triangles

Every triangle has three sides, in this case a, B and C and three angles. Angle a angle. Be an angle, see? So let's see what we're told and what we need to find. We were told that angle A is 68.41 degrees. Angle B is 54.23 degrees, and side A is 12.75 feet. So you can see from this that we're missing one angle and two sides. Let's start with the angle first. The sum of the angles in a triangle is always 180 degrees. So to find our missing angle, we take 100 and 80 degrees and subtract the two angles that I know, and that gives me a value of for angle See of 57.36 degrees. Now what about the sides? Well, as you can see, there's a pair that I know I know. Side A and angle A. Since I have a known pair, I can use the lot of signs, So let's start by finding Be first be divided by sine of angle. B equals a divided by sine of angles. A B equals A, which is 12.75 divided by sine of angles. A. An anklet is 68.41 degrees, and I'm going to multiply both sides by sign of Angle B, which is sign of 54.23 degrees. Evaluating that with your calculator gives a value for Side B of 11.13 feet. Now let's find our last unknown side see again. I can use the law of signs see divided by sine of angle. C equals a divided by sine of angles, A substituting what I know This fraction looks very similar to what we just had. 12.75 divided by sine of 68.41 degrees. This time, though, I'm going to multiply both sides by sign of angle, see which is sign of 57.36 degrees. Plugging that into your calculator, you get a value for side sea of 11.55 feet. Those are the three unknowns that were missing from our triangle

To begin this problem. Let's start with a sketch. That way we can see what we know and what we need. The first thing we know. Yes, we have angle a and that equals 96.80 degrees. I have Side B that equals 3.589 feet, and I have Side A, which is across the triangle from Angle A and that equals 5.818 feet. Angle B will be across the triangle from angle A from side B and angle. See is at the top of the triangle that the first question is, How many potential triangles do we have A is up to? So I have either zero or one potential triangles as long as a speaker than be. There is a triangle that exists, and it is society a can reach from angle see all the way down to Angle B. Well, that gives me three things that I know and three things that I need. I need to know angles, B and C as well aside to see. So how do we find these? Well, there's a pair of information that I know, I know. Angle A an side A so I can use the law of signs. I want my angle B so I'm going to put that on top of my proportion, and I'm going to set that equal to my proportion. Using a If I plug in the numbers that I know deck is me sign of 96.80 degrees, divided by a 5.818 and I'm going to multiply both sides by B 3.589 If I evaluate those numbers and then take the inverse sign that gives me a value for angle B of 37.77 degrees. Now on to our second unknown, let's deuce angle See, since every triangle has angles that add up to 180 degrees, I confined my unknown angle by subtracting from 1 80 the two angles that I do know in this case be and a and evaluating that gives me a value for angle see of 45.43 degrees. Now let's find our missing side. Since the side is what I'm looking for, I'm going to put that on the top of our proportion, this time substituting the values I know. I get 5.818 divided by sine of 96.80 degrees. And I'm gonna multiply both sides by sign of angle, see or 45.43 degrees and evaluating that gives me an value for side. See? Ah, 4.174 feet. Those are the three unknowns we need for this triangle.


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