Question

Using the triangle diagram below in the rules for special right triangles, discover the four missing links and choose them from the available choices:

Answer 1

The solution for the system of right triangles are, respectively:
`a = 2√(6)`,
`b = 4√(3)`,
`c = 4√(6)`,
`d = 6√(2)`

Explanation:

By Geometry, we get the following equivalencies:

`a = 2√(6)` (45 - 45 - 90 Theorem)

`b = √(2)\cdot (2√(6))` (45 - 45 - 90 Theorem)

`b = 4√(3)`

`c = (2√(6))/((1)/(2) )` (30 - 60 - 90 Theorem)

`c = 4√(6)`

`d = (2√(6))/((√(3))/(3) )` (30 - 60 - 90 Theorem)

`d = 6√(2)`