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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

8.1-正弦定律 Sine Rule [练习题]

(1)
Solve the following triangles, answers of angle correct to 1’, sides correct to 2 decimal places.
解下列各三角形, 其答案角度准确到1’, 边长准确到小数2位数。

(a) A = 40^{\circ}, B = 70^{\circ}, a = 7

(b) A = 35^{\circ}, B = 60^{\circ}, c = 5

(c) a = 6, b = 4, B = 30^{\circ}

(d) a = 5, b = 7, A = 30^{\circ}

(e) a = 5, b = 7, A = 60^{\circ}

答案 Answer :

(a) C = 70^{\circ}, b = 10.23, c = 10.23

(b) C = 85^{\circ}, a = 2.88, b = 4.35

(c) A = 48^{\circ}35’, C = 101^{\circ}25’, c = 7.84 or A = 131^{\circ}25’, C = 18^{\circ}35’, c = 2.55

(d) B = 44.43^{\circ}, C = 105.57^{\circ}, c = 9.63 or B = 135.57^{\circ}, C = 14.43^{\circ}, c = 2.49

(e) 无解

(2)

In \bigtriangleupABC, (a + b) : (b + c) : (c + a) = 3 : 4 : 5, find sinA : sinB : sinC.

\bigtriangleupABC中, (a + b) : (b + c) : (c + a) = 3 : 4 : 5, 求 sinA : sinB : sinC

答案 Answer :

2 : 1 : 3

(3)

If the angles of a triangle are in a ratio 1 : 6 : 3, and the perimeter of the triangle is 100cm, find the length of three sides.

若三角形的角的比例为1 : 6 : 3, 且该三角形的周长是 100cm,求三边长。

答案 Answer :

14.93cm, 45.97cm,39.10cm