Chapter 7 - Applications of Trigonometry and Vectors - Section 7.1 Oblique Triangles and the Law of Sines - 7.1 Exercises - Page 301: 12

$a = 10\sqrt 2$

1. Find $\angle B$ $\angle B = 180 - (\angle C + \angle A)$ $= 180 - (105 +45)$ $= 180 - 150$ $= 30^{\circ}$ 2. Find $a$ $\frac{a}{sin(45)} = \frac{10}{sin(30)}$ $a = \frac{10sin(45)}{sin(30)}$ $a = \frac{10(\frac{\sqrt 2}{2})}{\frac{1}{2}}$ $a = \frac{2(10(\frac{\sqrt 2}{2}))}{1}$ $a = 2(10(\frac{\sqrt 2}{2}))$ $a = 2(\frac{10\sqrt 2}{2})$ $a = 2(5\sqrt 2)$ $a = 10\sqrt 2$