Trigonometry word problem

Question

Frodo and Sam-wise Gangy are looking for a place to rest when Sam notices a bee hive up in a tree at

an angle of elevation of 36°

They walk 120 meters closer to get a better look and then look up at an

angle of elevation of 51°. Draw a picture and use Laws of Sine & Cosine to determine how far Frodo

and Sam are from the bottom of the tree from their current spot?

Answer 1

Want to find distance x

For the obtuse triangle

a = 120

∠B = 36º

∠C = 180º-51º = 125º

∠A = 180º-125º-36º = 19º

Using law of sines

c/sin(125º) = 120/sin(19º)

c = 301.923

For the large right triangle

cos(36º) = adjacent/hypotenuse = (120+x)/c = (120+x)/301.923 = 0.809

120+x = 301.923(0.809) = 244.26

x = 244.26-120 = 124.26 m