Question

The isosceles triangle has a base that measures 14 units. The value of y, the length of each leg, must be

Answer 1

Draw a median to the base. 

x = 7/cosy 

where , y angle between leg and base
x: leg

7 is half length of base.


x = 7/cosy


For cosy only positve (as leg length can only be a positive value) 


1 > |cosy| > 0  flip all sides

1 < 1/cosy < infinity    multiply times 7  

7 < 7/cosy < infinity


7/cosy = x

7 < x < infinity

To make that more discrete:

at cosy = cos 0 = 1

x = 7/1 = 7 (minimum) 

at cosy = cos60 = 0.5

x = 7/0.5 =14

at cosy = cos89 = 0.017

x = 7/0.017 = 401

but at cosy = cos90 = 0

x = 7/0 = infinity  (max point)

check the number line attached. 

greater than 7 

Answer 2

we know that

The Triangle Inequality Theorem states that the sum of any $2$ sides of a triangle must be greater than the measure of the third side

so

see the attached figure to better understand the problem

$AB=BC=y\ units \\ AC=14\ units$

1) $AB+AC > BC$

$x+14 > x$ -----> is ok

2) $AB+BC > AC$

$y+y > 14\\ 2y > 14\\y > 7\ units$

therefore

the answer is

The value of y must be greater than $7$