In triangle ABC from the corner c the height equal to 6 is drawn. AC = BC. Find AC if cosA = (√10) / 10.
| May 30, 2021 | education
Since CH is the height of the ABC triangle, the AСН triangle is rectangular.
Determine the sine of the angle CAB.
Sin2CAB = 1 – Cos2CAB = 1 – 10/100 = 90/100.
SinCAB = 3 * √10 / 10.
SinCAB = CH / AC.
AC = CH / SinCAB = 6 / (3 * √10 / 10) = 20 / √10 = 2 * √10 cm.
Answer: The length of the speaker side is 2 * √10 cm.
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