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. law of cosines: $a^2 = b^2 + c^2 - 2bc\cos(a)$ 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

Explanation:

Step1: Identify the values for the Law of Cosines

Let \(b = 650\), \(c=750\), and \(A = 60^{\circ}\). The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos(A)\).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Solve for \(a\)

\(a=\sqrt{497500}\approx705.34\)

Answer:

705 meters