In a right-angled triangle ABC, the angle is c = 90 degrees, AB = 10cm, the angle BAC = 60.

In a right-angled triangle ABC, the angle is c = 90 degrees, AB = 10cm, the angle BAC = 60. Find: a) ВС b) the height СD drawn to gypotinuse.

1. Considering that according to the properties of a right-angled triangle, the AC / AB ratio is the cosine of the angle at the vertex A, we calculate the length of the AC leg:

Cosine 60 ° = 1/2.

AC / AB = 1/2. AC = AB / 2 = 10/2 = 5 cm.

2. Angle ABC = 180 ° – 90 ° – 60 ° = 30 °.

3. Calculate the length of the BC leg:

ВС = √АВ ^ 2 – АС ^ 2 = √100 – 25 = 75 = 5√3 cm.

3. Considering that the leg CD, located opposite an angle of 30 °, is half the hypotenuse of the BC, we calculate its length:

СD = 5√3: 2 = 2.5√3 cm.

Answer: СD = 2.5√3 cm, ВС = 5√3 cm.