第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

8.2 余弦定律 Cosine 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 = 3, b = 6, c = 8

(b)  a = 10, b = 8, C = 30^{\circ}

Answer 答案:

(a)  A = 18.57^{\circ}, B = 39.56^{\circ}, C = 121.87^{\circ}

(b)  C = 5.04, B = 52.53^{\circ}, A = 97.47^{\circ}

(2)

In triangle ABC, the lengths of the sides AB, BC and CA are 7cm, 2cm and b cm respectively, and the size of angle C is 30^{\circ}. Use the cosine formula to show that b^2 - (2\sqrt{3})b - 45 = 0, and hence find the exact value of b. Hence, or otherwise, show that sinB= \frac{5\sqrt3}{14}

在三角形 ABC, AB, BC 和 CA 的边长分别为 7cm, 2cm and b cm, 及角C 为 30^{\circ}. 用余弦定律证明 b^2 - (2\sqrt{3})b - 45 = 0, 据此求 b 的准确值. 据此或其他方法,证明 sinB= \frac{5\sqrt3}{14}

Answer 答案:
5\sqrt{3}
(3)

b = a(\sqrt{3} + 1), C = 30^{\circ}, find A, B.

Answer 答案:
15^{\circ}, 135^{\circ}

(4)

Given that BD = 15, AB = 16, AD = 10 and \angleBDC = 30^{\circ}; find the angle of A and the length of BC.

已知BD = 15, AB = 16, AD = 10 和 \angleBDC = 30^{\circ}; 求角ABC的长度.         

Answer 答案:

65.83^{\circ}, 8.22

(5)

In \bigtriangleupABC, the lengths of the sides are three consecutive integers, the greatest angle is twice that of the least, find the lengths of sides of the triangles.

\bigtriangleupABCABC ,其边长为三连续整数,最大的角是最小的两倍,求三边长。
(提示:\sin{2\theta=2\sin{\theta}\cos{\theta}}

Answer 答案:

4, 5, 6

(6)

In a triangle ABC, a cosA = b cosB. Show that triangle ABC is a right angle triangle or isosceles triangle.
 
在三角形ABC, a cosA = b cosB.,试证三角形ABC是一个直角三角形或等腰三角形。