1. in the image below, (ad) ̅ is an angle bisector, (ab) ̅=42, (ac) ̅=35, and (bc) ̅=44. find the measure of m. show all your work. don’t forget to label your answer.

2. the area of a right triangle is 30 ft2. the base of the triangle is 12 ft. what is the length of the hypotenuse? show your work. don’t forget to label your answer.

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)