In a right-angled triangle, the leg opposite to the angle alpha is 8 cm.
| May 5, 2021 | education
In a right-angled triangle, the leg opposite to the angle alpha is 8 cm. Determine ctg ^ 2 alpha if the hypotenuse of the triangle is 16 cm.
Since the length of the hypotenuse AB is twice the length of the BC leg, AC / BC = 16/8 = 2, the angle α lying against the BC leg is 30.
The tangent of the angle α will be equal to: tgα = tg30 = √3 / 3.
Ctgα = 1 / tgα = 3 / √3, then ctg2α = 9/3 = 3.
Answer: ctg2α = 3.
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