(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 di
stance 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.
Draw a diagram to show the two lamp posts and Bob as shown below.
Let x = the angle formed from the lines from each lamppost to Bob. From the Law of Cosines, obtain 20² = 25² + 30² - 2(25)(30) cos(x) 400 = 625 + 900 - 1500 cos(x) 1500 cos(x) = 625 + 900 - 400 = 1125 cos(x) = 1125/1500 = 0.75 x = cos⁻¹ (0.75) = 41.4°