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°,
- The side opposite to the angle 30° = a
- The side opposite to the angle 60° = a√3
- The side opposite to the angle 90° = 2a
For triangle 45° - 45° - 90°,
- The side opposite to the angle 45° = a
- The side opposite to the angle 90° = a√2
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
