Geometry

Solving Triangles

Sine Rule - Ambiguous Case

         

How many distinct triangles are there such that a=6,c=15,A=30?a=6, c=15, \angle A=30^\circ?

Note: a,ba, b and cc are the lengths of the sides opposite the vertices A,A, BB and C,C, respectively.

How many distinct triangles are there such that a=20,c=16,A=30?a=20, c=16, \angle A=30^\circ?

Note: a,ba, b and cc are the lengths of the sides opposite the vertices A,A, BB and C,C, respectively.

How many distinct triangles are there such that A=30,a=9,b=93?\angle A=30^\circ, a=9, b=9\sqrt{3} ?

Note: a,ba, b and cc are the lengths of the sides opposite the vertices A,A, BB and C,C, respectively.

In triangle ABCABC, a=133a=13\sqrt{3}, b=13b=13, B=30\angle B=30^{\circ}, and C\angle C is acute. What is the value of C\angle C (in degrees)?

Details and assumptions

aa, bb and cc are the lengths of the sides opposite to the vertices AA, BB and CC, respectively. An acute angle is an angle strictly less than 9090^\circ.

How many distinct triangles are there such that a=35,b=56,A=30?a=35, b=56, \angle A=30^\circ?

Note: a,ba, b and cc are the lengths of the sides opposite the vertices A,A, BB and C,C, respectively.

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