Question

Dayton is due north of Richmond, and Easton is 16 mi due east of Richmond. Dayton is 32 mi from Easton.

How far apart are Dayton and Richmond? Round to the nearest tenth of a mile.


mi

Answer 1

Given:
                          Dayton
                                             --32 mi--                                                                                                   
                                                                                                                                                Richmond  -- 16 mi--           Easton


I can't draw a line but the figure drawn based on the given description is a RIGHT TRIANGLE.

Richmond to Easton is the short leg.
Dayton to Easton is the hypotenuse.
Richmond to Dayton is the long leg.

We are looking for the measure of the long leg. We will use the Pythagorean theorem.

a² + b² = c²
a² + 16² = 32²
a² + 256 = 1,024
a² = 1,025 - 256
a² = 768 mi²
a = √768 mi²
a = 27.71 mi   This is the distance of Dayton from Richmond

Answer 2

D
|
|
|
|
R ---------E

RE = 16mi
DE = 32 mi

DR^2 = DE^2 - RE^2 = (32mi)^2 - (16mi)^2 = 768 mi^2

DR = √(768 mi^2) = 27.7 mi