The diagonal of rectangle ABCD measures 2 inches in length.What is the length of line segment AB? 1 inch inches 4 inches inches

Question

asked Apr 16, 2018 89.5k views

2 Answers

Wasatz · Answer 1 · 2018-04-20T05:18:57+0000

we know that

AB=CD

AD=BC

in the right triangle DBC

$cos\ 30=(adjacent\ side\ angle\ 30)/(hypotenuse)$

$adjacent\ side\ angle\ 30=DC\\ hypotenuse=BD=2\ in$

substitute

$cos\ 30=(DC)/(2)$

$DC=2*cos\ 30\\\\DC=2*(√(3) )/(2) \\\\ DC=√(3)\ in$

$DC=√(3)\ in=1.73\ in$

remember that

AB=CD

so

$AB=√(3)\ in=1.73\ in$

therefore

the answer is

the length of line segment AB is
$√(3)\ in$