Question

question 11 of 25
a boat is 400 feet away from one dock and 300 feet away from another dock. the angle between the two paths is 45°. what is the approximate distance between the docks?
a. 383 feet
b. 183 feet
c. 283 feet
d. 551 feet

Explanation:

Step1: Recall the Law of Cosines

The Law of Cosines formula is $c^{2}=a^{2}+b^{2}-2ab\cos C$, where $a = 400$, $b = 300$, and $C=45^{\circ}$, and $\cos45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707$.

Step2: Substitute values into formula

$c^{2}=400^{2}+300^{2}-2\times400\times300\times\cos45^{\circ}$.
$c^{2}=160000 + 90000-240000\times0.707$.
$c^{2}=160000+90000 - 169680$.
$c^{2}=80320$.

Step3: Find the value of $c$

$c=\sqrt{80320}\approx 283.4$. Rounding to the nearest whole - number gives $c\approx283$ feet.

Answer:

A. 383 feet