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}-2bccos a) rounded to the nearest meter, what is the distance between the docks? round to the nearest meter. 529 meters 705 meters 792 meters 861 meters

Explanation:

Step1: Identify values for 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 values into formula

$a^{2}=650^{2}+750^{2}-2\times650\times750\times\cos(60^{\circ})$
$a^{2}=422500 + 562500-2\times650\times750\times\frac{1}{2}$
$a^{2}=422500+562500 - 487500$
$a^{2}=497500$

Step3: Solve for $a$

$a=\sqrt{497500}\approx705.34$
Rounding to the nearest meter, $a\approx705$

Answer:

705 meters