I need the answers to x & y for #14-18 . help pleaseee

14) The values of x= 7√3 and y= 14

15) The values of x= 16 and y= 16√3

16) The values of x= 3√2 and y= 3√2

17) The values of x= 11 and y= 22

18) The values of z= 24  x= 48/√3 and y= 24/√3

Step-by-step explanation:

The properties of Special Triangles :

For triangle 30° - 60° - 90°,

For triangle 45° - 45° - 90°,

14) The given triangle is 30° - 60° - 90°.

The side opposite to the angle 30° ⇒ a = 7

x is the side opposite to the angle 60° ⇒ a√3 = 7√3

y is the side opposite to the angle 90° ⇒ 2a = 14

15) The given triangle is 30° - 60° - 90°.

The side opposite to the angle 90° ⇒ 2a = 32

⇒ a = 32/2

⇒ a = 16

x is the side opposite to the angle 30° ⇒ a = 16

y is the side opposite to the angle 60° ⇒ a√3 = 16√3

16) The given triangle is 45° - 45° - 90°.

The side opposite to the angle 90° ⇒ a√2 = 6

⇒ a = 6/√2

⇒ a = 3√2

x and y are the sides opposite to 45° ⇒ a

Therefore, x = 3√2 and y = 3√2

17) The given triangle is 30° - 60° - 90°.

The side opposite to the angle 60° ⇒ a√3 = 11√3

⇒ a = 11

x is the side opposite to the angle 30° ⇒ a = 11

y is the side opposite to the angle 90° ⇒ 2a = 22

18) The left half of the triangle is 45° - 45° - 90°.

The side opposite to the angle 90° ⇒ a√2 = 24√2

⇒ a = 24.

z is the side opposite to 45° ⇒ a = 24

The right half of the triangle is 30° - 60° - 90°.

The side opposite to the angle 60° ⇒ a√3 = 24

⇒ a= 24/√3

x is the side opposite to the angle 90° ⇒ 2a = 48/√3

y is the side opposite to the angle 30° ⇒ a = 24/√3

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