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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. The distance between the docks is____ Rounded to the nearest meter.
A) 589
B) 705
C) 792
D) 861

Respuesta :

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using the cosine law

Cos60 = (650^2 +750^2 - x^2)/(2*650*750)     x is the distance between them

(2*650*750)cos60 = 650^2 + 750^2 - x^2

x^2 = 650^2 +750^2 - (2*650*750)cos60 =497500

x = √497500 = 705 meters approx.

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

Distance between the lifeguard and the first beach = 650 meters

Distance between the lifeguard and the second beach = 750 meters

As shown in the figure below :

We will use "Cosine formula ":

We need to find the distance between the docks is given by

[tex]\cos A=\frac{b^2+c^2-a^2}{2bc}\\\\\cos 60\textdegree=\frac{650^2+750^2-x^2}{2\times 650\times 750}\\\\\frac{1}{2}=\frac{422500+562500-x^2}{975000}\\\\\frac{975000}{2}=985000-x^2\\\\487500-985000=-x^2\\\\497500=x^2\\\\\sqrt{497500}=x\\\\705.33=x\\\\x=705\ meters[/tex]

Hence, Option 'B' is correct.

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