Question

question
allison heads out on a three - day sailing trip. on the first day, she sails 45 miles east and 15 miles north. on the second day, she leaves from the exact location she ended the day before and makes it 35 miles east and 30 miles south. on the third day, she gains another 15 miles east and 55 miles south. at the end of her final day, how far is she from her initial starting point? round your answer to the nearest whole number.
select the correct answer below:
o 97 miles
o 118 miles
o 134 miles
o 195 miles

Explanation:

Step1: Calculate total east - west displacement

Add up east - ward displacements. East is positive. She sails 45 + 35+15 = 95 miles east. There is no west - ward displacement. So the total east - west displacement $x = 95$ miles.

Step2: Calculate total north - south displacement

Add up north - south displacements. North is positive and south is negative. She sails 15 miles north and (30 + 55)=85 miles south. So the total north - south displacement $y=15−85=- 70$ miles.

Step3: Use the distance formula

The distance $d$ from the starting point is given by the distance formula $d=\sqrt{x^{2}+y^{2}}$. Substitute $x = 95$ and $y=-70$ into the formula: $d=\sqrt{95^{2}+(-70)^{2}}=\sqrt{9025 + 4900}=\sqrt{13925}\approx118$ miles.

Answer:

118 miles