In a right-angled triangle ABC with a hypotenuse of AC equal to 12 cm, the height BD is drawn. Find CD and DA if A = 30.
| September 26, 2021 | education
In a right-angled triangle ABC, the BC leg lies opposite the angle 30, then its length is equal to half the length of the AC hypotenuse.
BC = AC / 2 = 12/2 = 6 cm.
The ВСD triangle is rectangular, since ВD is the height, then the angle ВСD = (90 – 60) = 30.
The CD leg lies opposite an angle of 30, then its length is equal to half the length of the BC hypotenuse.
СD = ВС / 2 = 6/2 = 3 cm.
AD = AC – CD = 12 – 3 = 9 cm.
Answer: The length of the segment CD is 3 cm, the length of AD is 9 cm.
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