(50 POINTS) Bob is standing 25 feet from a lamppost that is to his left and 30 feet from a lamppost that is to his right. The distance between the two lampposts is 20 feet. What is the measure of the angle formed from the line from each lamppost to Bob? Approximate to the nearest degree.

 Letpoint A----------------- > Bob point B----------------- > lamppost that is to Bob left point C----------------- > lamppost that is to Bob right we know that dAB=25 ft dAC=30 ft dBC=20 ft see the attached figure we use the law of cosines------------- > dBC²=dAB² +dAC² -2(dAB)(dAC)cos(alfa) we have that 20²=25² +30² -2(25)(30)cos(alfa)-------- > cos (alfa)=(20²-(25² +30²))/(-2*25*30) cos (alfa)=(400-(625 +900))/(-1500)= (400-(625 +900))/(-1500)=1125/1500=0.75 alfa=arccos (0.75)=     41.4096 -------- > 41 °-------- > ∡ BAC  the answer is 41 °