Question

Find the length of x and y in the following figure.

Answer 1

Step 1:

The triangle has a right angle at the top (where sides x and y meet).

The angle at the bottom right is 30°.

The base of the triangle is 4.

So, this is a 30°–60°–90° right triangle.

Step 2: Properties of a 30°–60°–90° triangle

Opposite 30° : Opposite 60° : Hypotenuse = 1 : `sqrt3 : 2`

Step 3:

The side opposite 30° x.

The side opposite 60° y.

The side opposite 90° 4.

x : y : 4 = 1: `sqrt3 : 2`

Step 4:

Solve for x and y

Since the hypotenuse corresponds to 2, scale factor = `4/2` = 2

x = 1 × 2 = 2

y = `sqrt3 xx 2`

= `2sqrt3`

x = 2, y = `2sqrt3`