Question 1091197: How many triangles can be formed if side a = 17 ft? In triangle ABC, A = 60°, and side c = 18 ft.
Select one:
a. 0
b. 2
c. 3
d. 1
Found 2 solutions by math_helper, MathTherapy:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! d. 1 looks correct
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Using the Law of Sines:
sin(A)/a = sin(B)/b = sin(C)/c
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Since A=60 degrees, a=17ft, and c=18ft are given, one can compute C=54.876 degrees directly and then using A+B+C = 180, angle B can be found to be 65.124 degrees. The values given constrain the solution to one specific triangle.
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EDIT 8/25/17: Yes, MathTherapy is correct, there are TWO triangles (thanks MathTherapy for pointing it out). I made a calculation error in the computation of angle C, it should be 66.5 degrees (and hence the triangle with c=18, C=66.5 degrees is indeed valid). More importantly, I missed sin(C) = sin(180-C) and that gives you a 2nd triangle (one triangle has A,B,C = 60, 53.5, 66.5 degrees with sides a,b,c = 17, 15.78, 18 feet, respectively. The 2nd triangle has A,B,C = 60, 6.5, 113.5 degrees, with sides a, b, c = 17, 2.222, 18 feet, respectively). I'd change that to "answer 'b' looks correct."
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! How many triangles can be formed if side a = 17 ft? In triangle ABC, A = 60°, and side c = 18 ft.
Select one:
a. 0
b. 2
c. 3
d. 1
Two (2) triangles can be formed, so correct answer is:  .
FYI: Since side c > side a, then ∡C CAN NEVER be less than ∡A, as suggested by the other person who responded.
Therefore, IGNORE that answer as it's WRONG/INCORRECT/RIDICULOUS, etc.
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