In triangle ABC AC = BC, altitude CH = 6, cosA = √10 / 10. Find AB.
| September 27, 2021 | education
Determine the sine of the angle ABC.
Sin2CAB = 1 – Cos2CAB = 1 – 10/100 = (100 – 10) / 100 = 90/100 = 9/10.
SinCAB = 3 / √10.
Determine the tangent of the angle СAН. tgCAH = SinCAH / CosCAH = (3 / √10) / (√10 / 10) = 3.
In a right-angled triangle АСН tgCAH = СН / АН.
AH = CH / tgCAH = 6/3 = 3 cm.
The height of CH is also the median of the triangle ABC, then AB = 2 * AH = 2 * 2 = 4 cm.
Answer: The length of the base AB is 4 cm.
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