Question

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

Answer 1

Answer:

x = 8 √3

y = 8

Step-by-step explanation:

Here, we want to find the missing side length from the diagram

From the diagram let us identify each side

16 is the side that faces the right-angle and it is the longest side referred to as the hypotenuse

x is the side facing the angle given which is 60 degrees and is referred to as the opposite

The third side measuring y is the adjacent

To get x, we can link the hypotenuse and the opposite using the angle given

The measure of the sine of an angle is the ratio of the length of the opposite to that of the hypotenuse

Mathematically in this case;

sin 60 = x/16

x = 16 sin 60

x = 16 * √3/2

x = 8 √3

Lastly we want to get the third side marked y

Here, we can use the Pythagoras’ theorem

It states that the square of the length of the hypotenuse equals the sum of the squares of the two other sides

Thus, we have that;

16^2 = y^2 + (8 √3)^2

256 = y^2 + 192

y^2 = 256 -192

y^2 = 64

y = √64

y = 8