Question

Two teams are pulling heavy chest located at point X. The teams are 4.6 meters away from eachother. Team A is 2.4 meters away from the chest, and team B is 3.2 meters away. Their ropes are attached at an angle of 110°. Which equaton can be used to be solved for angle A.

Answer 1

We have a triangle with sides a=2.4 m, b=3.2 m and c=4.6 m and angle A=110° between the rope a and b. To find the angle A we can use the the law of cosines:   

c²=a²+b²-2*a*b*cosA.

Here we solve for cosA:

c²-a²-b²=-2*a*b*cosA

cosA=(c²-a²-b²)/-2*a*b=-0.336, now we take the inverse cosine:

cos⁻¹(cosA)=cos⁻¹(-0.336) and get:

A=109.62° which is very close to 110°.

So the correct answer is: we need the law of cosines to solve for angle A.