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Solve the triangles with the given parts.$$a=385.4, b=467.7, c=800.9$$...

Question

Solve the triangles with the given parts.$$a=385.4, b=467.7, c=800.9$$

Solve the triangles with the given parts. $$a=385.4, b=467.7, c=800.9$$



Answers

Solve the triangles with the given parts. $$a=385.4, b=467.7, c=800.9$$

Let's catch the triangle, ABC, with the information given. So it's pretty. See here. All right, so a is give not given. B is 29 29 degrees. She's 51 degrees, small bees 44 and this is a C. This is a all right. Let's start by finding angle angle A is 1 80 minus 29 minus 51 so that will be equal to 100 degrees. So we found a. Now let's move to the loo in the loft signs so signed 100 over small A is equal to sign. 51 Oversee is equal to sign 29/44. So let's find a first A is signed 100 divided by signed 29/44. In that case, they will be equal to 89. All right now see is sign 51 divided by signed 29/44. Solving for this sea will be equal to 71. Those are all your answers

Action here were given that tango Alfa here is equal to 39.6 degrees side C has length and team 0.4 and beside opposite of A, has a length of 3.7. So what we first need to do is find our height. If we were to imagine any perpendicular line going down like this we have the height is equal to 18.4 times Sign of Alfa, which is 39.6. You get to this sequel to 11.73 So we know that is you could 3.7, which is less than 11.73 So you a is less than each. And this means that we have no triangle that fits this description. So that is our answer.

The situation here were given that the ankle beta is the 28.6, beside opposite of beta B is equal to 52.5 in length and a is 40.7. And link because you could already see B, which is 52.5 is greater than A, which is 40.7. To that automatically means that we have one triangle, one possible triangle. So if we were to draw out this trial here we get the new It looks like this where a is again 40.7 beta here is 28.6 and a here is 52.5, so we can find out what this angle here across from a single to using all signs. You know that 52 0.5, divided by sign of 28.6 is equal to 40.7 divided by sign of that angle. Let's call it Alfa. So this means that if we cross multiply, we get 52.5 Sign of Alfa. Did you go to 40.7? Comes side of 28.6, not dividing both sides by 52.5 and then finding the inverse sine of each side we get that Alfa is equal to the inverse sine 0 40.7 time sign of 28.6 divided by 52 0.5. Now, in order to solve for awful here you can petition to the calculator and we again. Is that Alfa approximately 21.8. So this is 21.8. This means that this very final angle here is equal to 1 29.6 So if we were to call this side see, you know that C divided by the sine 01 29.6 is equal to 52.5, provided by the sign 28.6 Now, in order to solve for C here, we can cross, multiply, can or we can use multiply both sides by the sign. Oh, 129 0.6. And what you get is that C is equal to 84.5. So what are finally triangle here? Looks like we have a big triangle here, 40.7 for a be easy with the 52.5. See easy go to 84.5 this angle here is 1 29 point try or 2.6. The single here's 21.8 and the single. Here it is 28.6.

This question here were given that we have an angle on acute angle Alfa, which is equal the 75.3 degrees and aside a equal to 12.4 and decide be equal to 9.8 and length. Since A is greater than be here, we can say we have one possible triangle and we could draw this triangle like this where a is 12.4 here now our first up we could do is to solve for beta here because we know that 9.8, which is be divided by the sine of beta physical to 12.4, divided by the sine of 75.3, know solving for beta. What you get is 49.9 degrees for beta here, which means that we can solve for this last angle. Let's call a gamma on the side. See gamma here is equal to 1 80 minus 75.3, minus 49.9, which is equal to 54.8. So we can again use the law signs to find what link of C. So we know that C divided by the sine of gamma is equal to 12 point for a divided by the sine of Alfa. So if we use our calculators, what we can do to solve for C Do 12.4 divided by the son of Alfa, which we know is equal 2 75.3 Then if we multiply both sides by the sign of gamma here we can't the most pious by sign of 54.8, which is equal to a 10.5. How's our finals?


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