In triangle ABC AC = BC = 54, angle C is 30 degrees Find the height AH.

univerkov | September 19, 2021 | education

The angles of triangle ACH add up to 180 degrees, so
180 = angle (ACH) + angle (CAH) + angle (AHC).
angle (CAH) = 180 – 90 – 30 = 60 degrees.
triangle AHC is right-angled and AC is hypotenuse, therefore
AH = AC * cos (CAH) = 54 * 0.5 = 27 cm.
Answer: 27 cm.

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