Using the Law of Sines to find a triangle with one obtuse angle if ∠A=50∘,a=25,b=28.If no answer exists, enter DNE for all answers.

Question

Using the Law of Sines to find a triangle with one obtuse angle if If no answer exists, enter DNE for all answers.

 is Incorrect   degrees;

 is Incorrect   degrees;

    

Answer 1

1. draw the triangle with what you know
2. Law of Sines: Sin A/a = Sin B/b = Sin C/c Caps are angles, lower case are legs opposite angle
3. Start with what you've been given: Sin 50/25 = Sin B/28 and solve for B
4. Sin B = (28) Sin 50/25 = .8579...
5. B = Sin^-1(.8579....); B = 59.09° Hey, not obtuse! BUT you would get the same answer if the angle for B was 120.91° (Sine is + in the 2nd quadrant; so 180-59.09 = 120.91)
6. Now you can find angle C (all triangle angles sum to 180°); C = 9.09°
7. Use what you were originally given for the last leg to solve (c)
8. Sin50/25 = Sin 9.09/c cross multiply and solve for c
9. c = 5.16
10. do a check to make sure the 2 smaller legs (b and c) are greater than leg a (check).

This triangle can exist.