Final answer:
Two triangles can be formed.
Step-by-step explanation:
To determine how many triangles can be formed with two sides of lengths 17 and 19, and an opposite angle measuring 5°, we can use the Law of Sines.
This law states that the ratio of the sine of an angle to the length of the side opposite that angle is constant for all angles in a triangle. In this case, we can use the formula:
sin(A)/a = sin(B)/b = sin(C)/c
Where A, B, and C are the angles in the triangle, and a, b, and c are the lengths of the opposite sides. Since we are given the lengths of two sides and the measure of the angle opposite the longer side, we can set up the equation:
sin(5°)/17 = sin(B)/19
To solve this equation, we can cross-multiply and then take the inverse sine to find the measure of angle B. There will be two possible angles for B, corresponding to two possible triangles.
Therefore, two triangles can be formed.