In triangle ABC, angle C = 90 *, angle A = 30 *, Ac = 19√3. Find BC.
| August 11, 2021 | education
Half of the hypotenuse lies in a right-angled triangle opposite an angle of 30 °.
So 2 * BC = AB.
AC ^ 2 + BC ^ 2 = AB ^ 2,
(19√3) ^ 2 + (AB / 2) ^ 2 = AB ^ 2,
4 * 19 * 19 * 3 + (AB) ^ 2 = 4 AB ^ 2,
3 AB ^ 2 = 4 * 19 * 19 * 3,
AB ^ 2 = 4 * 19 * 19,
AB = 2 * 19,
AB = 38.
BC = AB / 2 = 38/2 = 19.
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