Question

(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.

Answer 1

 Let

point 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 °

Answer 2

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°

Answer: 41° (nearest degree)