Answer:
DC = 2
Step-by-step explanation:
From the diagram, AD (i.e the angle bisector) bisects the angle into 2 equal parts. Thus, BD and DC are equal.
BD = 2
DC = BD = 2
DC = 2
This can further be explained as illustrated below:
We'll begin by calculating AD. This can be obtained as follow:
Angle A = 30°
Opposite = BD = 2
Hypothenus = AD =?
Sine A = Opposite (BD) /Hypothenus (AD)
Sine 30 = 2 / AD
0.5 = 2 / AD
Cross multiply
0.5 × AD = 2
Divide both side by 0.5
AD = 2 / 0.5
AD = 4
Finally, we shall determine DC. This can be obtained as follow:
Angle A = 30°
Hypothenus = AD = 4
Opposite = DC =?
Sine A = Opposite (DC) /Hypothenus (AD)
Sine 30 = DC / 4
Cross multiply
DC = 4 × Sine 30
DC = 4 × 0.5
DC = 2
