Question

What is the length of x

Answer 1

We have a 45-45-90 triangle with hypotenuse

`24 √(6) \: \: \: leg \: x \: therefore \: has \: length \\ (24 √(6) )/( √(2 \:) \: ) \: = \: (24 √(3) √(2) )/( √(2) \: ) = 24 √(3) = x \\ \\`
We now work with the 30-60-90. triangle having a side opposite the 60 degree angle of length

`24 √(3)`
y, the side opposite the 30 degee angle then has length

`(24 √(3) )/( √(3)) = 24`
The hypotenuse has length twice the side opposite the 30 degree angle = 2y = 48 = z