1.A ship sees a lighthouse which is found to be 9.8 km distant through the use of radar. The lighthouse is 3km from a second lighthouse. The angle between the line of sight between the two lighthouses is 30°. What is the angle between the line of sight between the ship and lighthouse 2, when looking from lighthouse 1?
2.In a triangle ABC, side a is 18cm long, side b is 10cm long and angle B is 89°. What is the measure of angle A?
To #1:
You know 2 sides and one angle of the triangle in question. The angle is opposite the smaller side. Thus you can't draw congruent triangles with the given properties, because for the congruence rule SSA the given angle has to be opposite the greater side (of the two given sides).
To your drawing: Your angle of 30° is correct for very small values of 30 . I've attached an acurate drawing with all measures.