Determine the number of possible triangles with the given information

Question

a = 6, b = 5, α = 25°

a. One

b. Two

c. Three

Answer 1

h = b sin (alpha) = 5 * sin(25) = 2.11

angle alpha is less than 90 degrees, so we have the acute case, which provides following situations:

0 < a < h ---> 0 triangles is 0 < 6 < 2.11 NO

a = h ---> 1 triangle does 6 = 2.11 NO

h < a < b ---> 2 triangles is 2.11 < 6 < 5 NO

a >= b ---> 1 triangle is 6 >= 5 YES

so there is one triangle