The height AH of the right-angled triangle ABC drawn to the hypotenuse is 7 cm, and the angle C is 60
| August 22, 2021 | education
The height AH of the right-angled triangle ABC drawn to the hypotenuse is 7 cm, and the angle C is 60 degrees. Find AB.
Since the sum of the acute angles of a right-angled triangle is 90 °, ∠B + ∠C = 90 °.
Find ∠B.
∠B = 90о – ∠C.
∠B = 90 ° – 60 ° = 30 °.
AH is the height, so AH ┴ BC. ∠AHB = 90o, so ΔAHB is rectangular.
sin∠B = AH / AB.
AB = AH / sin∠B.
sin∠B = sin30о = 1/2.
AB = 7: 1/2 = 7 * 2/1 = 7 * 2 = 14 (cm).
Answer: 14 cm.
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