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2011-04-08 3:24 am

1. In△ABC,a=7cm,b= k cm and A=52°.Find the range of the values of k such that a triangle can be constructed with the given information.

2.Find angle BAD

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回答 (1)

用戶2053

2011-04-08 4:22 am

✔ 最佳答案

1)a / sinA = b / sinB7 / sin52° = k / sinBk = sinB (7 / sin52°)Since 0° < B < 180 - 52 = 128° ,the maximum value of sinB = sin90° = 1
the minimum value of sinB = sin0° = 0
Sosin0° (7 / sin52°) < k < sin90° (7 / sin52°)0 < k < 7 / sin52° 2)Let BD = DC = x ,AC / BC = tan 25°AC / (2x) = tan 25° .....(1)AC / DC = tanㄥADC
AC / x = tan(ㄥBAD + 25°) ......(2)(2) / (1) :2 = tan(ㄥBAD + 25°) / tan 25°2 tan 25° = tan(ㄥBAD + 25°) 0.93262 = tan(ㄥBAD + 25°) ㄥBAD + 25° = 43°ㄥBAD = 18°

2011-04-07 20:29:06 補充：
1)

0 < k ≤ 7 / sin52°

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