Question

A boat is 500 feet away from one dock and 600 feet away from another dock the angle between the two paths is 45. What is the approximate distance between the docks

Answer 1

check the picture below.

$\bf \textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)cos(C)\implies c = \sqrt{a^2+b^2-(2ab)cos(C)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} a=500\\ b=600\\ C=45^o \end{cases}\implies c=\sqrt{500^2+600^2-[2(500)(600)]cos(45^o)} \\\\\\ c=\sqrt{610000-600000\cdot \frac{\sqrt{2}}{2}}\implies c\approx \sqrt{185735.93}\implies c\approx 430.97$

Answer 2

Answer:

431 ft

Step-by-step explanation:

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