Question

Analyze the diagram below and complete the instructions that follow.

Find the value of x and the value of y.
A. X= 23.y=413
B. 1 = 3, y = 613
C. = 6/3, y = 12
D. x= 23, y = 6

Answer 1

x =
`2√(3)` , y =
`4√(3)` ⇒ A

Explanation:

In the 30°-60°-90° triangle, there is a ratio between its three sides

• The length of the side opposite to the angle of measure 30° is half the length of the hypotenuse

• The length of the side opposite to the angle of measure 60° is half the length of the hypotenuse times
  `√(3)`

→ 30° : 60° : 90°

→ 1 :
`√(3)` : 2

In the given figure

∵ The length of the hypotenuse is y

∵ The length of the side opposite to the angle of measure 30° is x

∵ The length of the side opposite to the angle of measure 60° is 6

→ By using the ratio above

→ 30° : 60° : 90°

→ 1 :
`√(3)` : 2

→ x : 6 : y

→ By using cross multiplication

∵ x ×
`√(3)` = 1 × 6

∴ x
`√(3)` = 6

→ Divide both sides by
`√(3)`

∴ x =
`(6)/(√(3))`

→ Simplify it by multiplying up and down by
`√(3)`

∴ x =
`(6√(3))/(3)=2√(3)`

∴ x =
`2√(3)`

∵ y ×
`√(3)` = 6 × 2

∴ y
`√(3)` = 12

→ Divide both sides by
`√(3)`

∴ y =
`(12)/(√(3))`

→ Simplify it by multiplying up and down by
`√(3)`

∴ y =
`(12√(3))/(3)=4√(3)`

∴ y =
`4√(3)`