Question

question
a fox leaves its den and travels 925 yards southeast, then 750 yards west. how far, in yards, is the fox from its den? round your answer to the nearest hundredth.
sorry, thats incorrect. try again?
yards

Explanation:

Step1: Resolve southeast - direction components

The southeast - direction is at a 45 - degree angle. The east - west and north - south components of the 925 - yard southeast displacement are $925\cos45^{\circ}$ and $925\sin45^{\circ}$ respectively. Since $\cos45^{\circ}=\sin45^{\circ}=\frac{\sqrt{2}}{2}$, the east - west component of the 925 - yard displacement is $925\times\frac{\sqrt{2}}{2}\approx925\times0.7071 = 654.07$ yards east and the north - south component is also approximately 654.07 yards south.

Step2: Calculate the net east - west displacement

The fox then travels 750 yards west. The net east - west displacement $x$ is $654.07−750=- 95.93$ yards (negative means west). The north - south displacement $y = 654.07$ yards south.

Step3: Use the Pythagorean theorem

The distance $d$ from the starting point (the den) is given by the Pythagorean theorem $d=\sqrt{x^{2}+y^{2}}$. Substitute $x=-95.93$ and $y = 654.07$ into the formula: $d=\sqrt{(-95.93)^{2}+654.07^{2}}=\sqrt{9192.56 + 427806.56}=\sqrt{436999.12}\approx602.91$ yards.

Answer:

602.91