To solve the triangle, we need to find the lengths of all sides and the measures of all angles. We are given:
A = 9 (length of side opposite angle A)
B = 49° (measure of angle B)
We can find angle A using the Law of Sines:
a/sin A = b/sin B
where a and b are the lengths of the side opposite and angle adjacent to angle A, respectively. Plugging in the given values, we get:
9/sin A = b/sin 49°
We still need to find the length of side b. To do this, we can use the fact that the angles in a triangle sum to 180°:
A + B + C = 180°
C = 180° - A - B
C = 180° - 9 - 49°
C = 122°
Now we can use the Law of Sines again to find the length of side b:
b/sin B = c/sin C
where c is the length of the side opposite angle C. Plugging in the known values, we get:
b/sin 49° = c/sin 122°
We can rearrange this equation to solve for b:
b = (sin 49° / sin 122°) c
We still need to find the length of side c. To do this, we can use the fact that the sides opposite equal angles are equal in length. Since we know the measures of angles A and B, we know that the side opposite angle B is b, so the side opposite angle A must be 9. Therefore, we have:
c = 9
Now we can plug in the known values to find the length of side b:
b = (sin 49° / sin 122°) (9)
b ≈ 6.02
Therefore, the sides of the triangle are A = 9, B ≈ 6.02, and C = 9, and the measures of the angles are A ≈ 8.9°, B = 49°, and C ≈ 122.1°.