In a right-angled triangle ABC with right angle C, the height CD is drawn. AC = 2cm, angle CAD = 60 Find AD.

1. S ΔАВС – area.

2. We calculate the length of the hypotenuse AB in terms of the cosine ∠A:

AC: AB = cosine ∠A = cosine 60 ° = 1/2.

AB = AC: 1/2 = 2: 1/2 = 4 centimeters.

3. ВС = √АВ² – АС² (by the Pythagorean theorem).

BC = √4² – 2² = √16 – 4 = √12 = 2√3 centimeters.

4. S ΔABC = BC x AC / 2 = 2√3 x 2/2 = 2√3 centimeters².

5. According to another formula S ΔABC = AB x CH / 2.

CH = 2S: AB = 2 x 2√3: 4 = √3 centimeters.

6. AD = √AC² – SD² = √2² – √3) ² = √4 – 3 = 1 centimeter.

Answer: the length of the blood pressure segment is 1 centimeter.