The city of Morgana is 20 miles due west of Vining. Beckett is due north of Morgana. If the distance from Beckett to Vining is 2 miles less than 3 times the distance from Beckett to Morgana, How far apart are Beckett and Morgana? Round to 1 decimal place.
A) 7.8 miles
B) 6.9 miles
C) 5.3 miles
D) 11.2 miles

Question

Quizplus · Accepted Answer

The distance from Beckett to Morgana can be represented as x. The distance from Beckett to Vining is given as 3x - 2. Since Morgana is 20 miles west of Vining and Beckett is directly north of Morgana, we can form a right triangle with Beckett, Morgana, and Vining. The distance from Morgana to Vining (20 miles) and the distance from Beckett to Vining (3x - 2) are the legs, and the distance from Beckett to Morgana (x) is the hypotenuse. Using the Pythagorean theorem: $x^2 = 20^2 + (3x - 2)^2$. Solving this equation for x gives approximately 7.8 miles.

The City of Morgana Is 20 Miles Due West of Vining