Question

kaito and cole are going to a concert together. the concert venue is 19 miles west and 9 miles south of kaitos house. coles house is 5 miles east and 15 miles north of kaitos house. if kaito meets cole at coles house, how far away from the concert venue are they? round your answer to the nearest tenth.

Explanation:

Step1: Find the horizontal and vertical distances from Cole's house to the concert venue

The horizontal distance from Cole's house to the concert venue: The concert venue is 19 miles west of Kaito's house and Cole's house is 5 miles east of Kaito's house. So the horizontal distance $x=19 + 5=24$ miles west. The vertical distance from Cole's house to the concert venue: The concert venue is 9 miles south of Kaito's house and Cole's house is 15 miles north of Kaito's house. So the vertical distance $y=15 + 9=24$ miles south.

Step2: Use the Pythagorean theorem

The distance $d$ between Cole's house and the concert venue is given by the Pythagorean theorem $d=\sqrt{x^{2}+y^{2}}$. Substitute $x = 24$ and $y = 24$ into the formula: $d=\sqrt{24^{2}+24^{2}}=\sqrt{2\times24^{2}}=24\sqrt{2}\approx24\times1.414 = 33.936\approx33.9$ miles.

Answer:

33.9 miles