Can somebody help me with these question ??

Question 1

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