Question

An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sink hole without falling in so you use congruent triangles. You have one piece of rope that is 50 ft. long and another that is 70 ft. long. You pick a point "A" on one side of the sink hole and "B" on the other side. You tie a rope to each spot and pull the rope out diagonally back away from the sink hole so that the two ropes meet at point "C" . Then you recreate the same triangle by using the distance from line "AC" and line "BC" and creating new segments CE and CD . The distance of line "DE" is 52.2 ft. 
What is the measure of angle ACB?

*I editted it because I realized I messed up a few things whoops

Answer 1

Triangle ABC and triangle DCE are congruent, so line DE = line AB

Use the cosine rule to find angle ACB
$52.2^{2}= 50^{2}+ 70^{2}-(2*50*70*cos(ACB))$
$2724.84=7400-(7000cos(ACB))$
$2724.84-7400=-7000cos(ACB)$
$-4675.16=-7000cos(ACB)$
$\frac{4675.16}{7000}=cos(ACB)$
$Angle ACB= cos^{-1} ( \frac{4675.16}{7000})$
Angle ACB = 48.1°