+0  
 
0
110
1
avatar

In trapezoid ABDC, AB = 5, DC=11. E is the midpoint of AB. F is the midpoint of DC. ∠D+∠C=90∘ . What is the length of EF?

 

 Jun 1, 2020
 #1
avatar+1387 
+1

Let the angle C be 60º, and the angle D be 30º

 

The height of the trapezoid we may denote with an h

 

AB = 5           CD = 11           EG = 1.5

 

h / tan(60º) + h / tan(30º) = 6                  ( 11 - 5 = 6 )

 

h / 1.732 + h / 0.57735 = 6       ( simplify )

 

0.57735 * h + 1.732 * h = 6

 

2.3094 * h = 6

 

h = 2.598077423

 

EF = sqrt ( h² + 1.5² ) = 3   indecision

 

 Jun 1, 2020
edited by Dragan  Jun 1, 2020
edited by Dragan  Jun 2, 2020

13 Online Users

avatar