suppose you have triangle ABC with sides a, b, c with the given measurements. Draw and solve the triangle. determine the area

Question

A= 75º, a=51.2, b=33.7

Answer 1

A = 75 degrees

b = 51.2

a = 33.7

use the Law of Sines

sinB/b = sinA/a

sinB/51.2 = sinA/33.7

sinB = 51.2(sin75)/33.7 = 51.2(.966)/33.7 >1 which is impossible

there is no triangle with an angle 75 and opposite side = 33.7 as well as another side = 51.2

or try the Law of Cosines

a^2 = c^2 + b^2 -2cbCosA

33.7^2 = c^2 + 51.2^2 - 2c(51.2)Cos75

solve for c

c^2 - 102.4(.259)c + 2621.44 - 1135.69

c^2 -26.52c + 1485.75 = 0

the discriminant = b^2 -4ac = 26.52^2 - 4(1485.75) <0

there is no real solution for side c

try drawing a rough sketch of the "triangle" You can't, not with 75 degrees, opposite side 33.7 and one other side = 51.2