Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.A = 61° a = 17 h = 19

Answer:The Law of Sines applies to any triangle and works as follows:a/sinA = b/sinB = c/sinCWe are attempting to solve for every angle and every side of the triangle. With the given information, A = 61°, a = 17, b = 19, we can solve for the unknown angle that is B.a/sinA = b/sinB17/sin61 = 19/sinBsinB = (19/17)(sin61)sinB = 0.9774sin-1(sinB) = sin-1(0.9774)B = 77.8°With angle B we can solve for angle C and then side c.A + B + C = 180°C = 180° - A - BC = 180° - 61° - 77.8°C = 41.2°a/sinA = c/sinC17/sin61 = c/sin41.2c = 17(sin41.2/sin61)c = 12.8The first solved triangle is:A = 61°, a = 17, B = 77.8°, b = 19, C = 41.2°, c = 12.8However, when we solved for angle B initially, that was not the only possible answer because of the fact that sinB = sin(180-B).The other angle is simply 180°-77.8° = 102.2°. Therefore, angle B can also be 102.2° which will give us different values for c and C.C = 180° - A - BC = 180° - 61° - 102.2°C = 16.8°a/sinA = c/sinC17/sin61 = c/sin16.8c = 17(sin16.8/sin61)c = 5.6The complete second triangle has the following dimensions:A = 61°, a = 17, B = 102.2°, b = 19, C = 16.8°, c = 5.6The answer you are looking for is the first option given in the question:B = 77.8°, C = 41.2°, c = 12.8; B = 102.2°, C = 16.8°, c = 5.6Step-by-step explanation: