In a right-angled triangle ABC, angle C = 90 degrees, angle A = 30 degrees CD-height, BD = 1 Find AD.

Consider a triangle ABC:

angle ABC = 180 ° – 90 ° – 30 ° = 60 °

Consider triangle CDB:

angle DCB = 180 ° – 90 ° – 60 ° = 30 °.

In a right-angled triangle, opposite an angle of 30 °, lies the leg BD, equal to half of the hypotenuse CB.

Thus:

BD = 1/2 * CB;

CB = 2 * BD = 2 * 1 cm = 2 cm.

Let’s go back to the ABC triangle:

Since the angle CAB = 30 °, the leg CB, equal to half of the hypotenuse AB, lies opposite the angle 30 °.

Then we get:

CB = 1/2 * AB;

AB = 2 * CB;

AB = 2 * 2 cm = 4 cm.

Now we find AD:

AD = AB – DB = 4 – 1 = 3 cm.

Answer: 3 cm.