Answer:
x = 8 √3
y = 8
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