Question

Using the technique in the model above, find the missing segments in this 30°-60°-90° right triangle. AB = 8 BC = 4 CD =

Answer 1

simpler version of answer above / below me

2 square root(3)

Answer 2

For a 30-60-90 triangle the sides always have the same relationship
Short leg = a
Long leg = a√3
Hypotenuse = 2a

BC is the short leg of ∆ABC

Given BC = 2
BC = a
Therefor
a = 2
AB = 2a = 4
AC = a√3 = 2√3

For ∆ACD
As above AC = 2√3
Since AC is the hypotenuse of ∆ACD
2a = 2√3
a = √3

CD = a = √3
AD = a√3 = 3

For ∆BCD
As above
BC = 2
CD = √3
Since BC is the hypotenuse of ∆BCD
2a = 2
a = 1

DB = a = 1