Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.

x = 4

y = 2

Step-by-step explanation:

Here, we want to find the given sides;

From the question;

x is the side that faces the right-angle and thus is the longest side. This is called the hypotenuse

The length 2 √3 faces the angle given and is called the opposite

Lastly the third side is called the adjacent and is represented by y

Let us work with the given angle

Mathematically, the sine of the given angle is the ratio of the opposite length to the length of the hypotenuse

thus;

sin 60 = 2 √3/x

x = 2 √3/sin 60

x = 4

Now, to get the value of y, we can use Pythagoras’ theorem

Mathematically, this states that the square of the hypotenuse equals the sum of the squares of the two other sides

We have this as;

4^2 = y^2 + (2√3)^2

16 = y^2 + 12

y^2 = 16-12

y^2 = 4

y = √4

y = 2

72 is the answer to this problem