Question

A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand.. Rounded to the nearest meter, what’s the distance between the docks in meters

Answer 1

did the assignment

Explanation:

A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand.

Law of cosines:

A triangle is created between a lifeguard stand and 2 floating docks. The distance from the lifeguard stand to one dock is 750 meters, and the distance to the second dock is 650 meters. The angle between the 2 sides is 60 degrees.

Rounded to the nearest meter, what is the distance between the docks? Round to the nearest meter.

589 meters

705 meters

792 meters

861 meters

Answer 2

we know that

Applying the law of cosines

c²=a²+b²-2*a*b*cos C

in this problem

c--------> is the the distance between the docks in meters

a---------> 650 meters

b--------> 750 meters

C---------> 60°

substitute in the formula above

c²=650²+750²-2*650*750*cos 60------> c²=497,500---------> c=705.34 m

c=705 meters

therefore

the answer is

the distance between the docks in meters is equal to 705 m