A triangle has sides A, B, and C. The angle between sides A and B is #pi/6# and the angle between sides B and C is #pi/12#. If side B has a length of 25, what is the area of the triangle? Trigonometry Triangles and Vectors Area of a Triangle 1 Answer sankarankalyanam May 3, 2018 #color(maroon)("Area of Triangle " A_t = 57.2 " sq units"# Explanation: #color(blue)("Given " hat A = pi/12, hat C = pi/6, hat B = pi - pi/12 - pi/6 = (3pi)/4, b = 25# #"As per " color(red)("Law of Sines", color(green)(a / sin A = b / sin B = c / sin C# #a / sin (pi/12) = 25 / sin ((3pi)/4) = c / sin (pi/6)# #c = (25 * sin (pi/6)) / sin ((3pi)/4) = 17.68# #"Area of " Delta = A_t = (1/2) *b * sin A# #A_t = (1/2) * 25 * 17.68 * sin (pi/12) = 57.2 " sq units"# Answer link Related questions How do you find the area of a triangle with 3 sides given? What is the area of a equilateral triangle with a side of 12? How do you find the area of a triangleABC, if #angleC = 62^@#, #b = 23.9# , and #a = 31.6#? How do you find the area of a triangleGHI, if #angleI = 15^@#, #g = 14.2# , and #h = 7.9#? What is Heron's formula? When do you use Heron's formula to find area? How do you find the area of a triangle ABC, if #a = 23#, #b = 46# , and #c = 41#? Question #f2e4c How do you find the area of the triangle given c= 4, A= 37 degrees, B= 69 degrees? How do you find the area of the triangle given C=85 degrees, a= 2, B= 19 degrees? See all questions in Area of a Triangle Impact of this question 1178 views around the world You can reuse this answer Creative Commons License