The values of ∠B, a and c in the triangle are 68°, 8.1 and 13
What is a triangle?
triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle. A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.
The sum of he interior angles of the triangle is 180°
so that, ∠A + ∠B + ∠C =180
37 + ∠B + 75 = 180
∠B = 180 - 112
∠B = 68°
Using sine rule to find a and c
a/sinA = b/sinB = c/sinC
tto find a
a/SinA = b/sinB
substitute A, B and b o fin a
a/sin37 = 12/sin68
cross multiply
a sin68 = 12 sin 37
a sin68 = 12(0.6018)
a(0.9271) = 7.221
a = 7.221/0.9271
a = 8.4
to find c
b/sin B = c / sin C
12/sin68 = c/sin75
cross multiply we have
c sin 68 = 12sin(75)
c(0.9271) = 12(0.9659)
c = 12.5
In conclusion the values of A, a and c are 68°, 8.4 and C 12.5
Learn more about sine rules: https://brainly.com/question/27174058
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