Question

For questions 10 and 11: (3 points cach) Solve the triangle 10. b = 7.c = 5, y = 37 e b Cs = SSA = LOS sinas sing sin & 5 Ein (27) 15 sin (37) Sino sing =3.01 Sin (3.01) = A a= be 7 5 3.01 ya 11. a=5,b= 6,0 = 4 3 C=4 a 5 S G ba BE 4 7

Answer 1

10. b = 7.c = 5, y = 37"

Using sine rule:

с b sin 8 sin


b sin sin B 7 sin 370 5 8 = sin-20.8414 = 57.4° 7 * 0.601 5 0.8414 с


From angle sum property:
Sum of the angle = 180
$\\37\degree+ 57.4\degree + \alpha = 180\degree\\ \alpha= 85.6\degree$

Again sing sine rule:

a sin a sin

$a = \frac{c\sin \alpha}{\sin \gamma} = \frac{7 \sin 57.4\degree}{\sin 37\degree} = \frac{7*0.842}{0.601} =9.8$

2.

11.25.b = 6.c = 4

Using cosine rule:
$\alpha = \cos^{-1}\left ( \frac{b^2+c^2-a^2}{2bc} \right )$
$\alpha = \cos^{-1}\left ( \frac{6^2+4^2-5^2}{2*6*4} \right ) =\cos^{-1}\frac{9}{16}$
$\alpha =55.77^{\circ \:}$


$\beta = \cos^{-1}\left ( \frac{a^2+c^2-b^2}{2ac} \right )$
$\beta= \cos^{-1}\left ( \frac{5^2+4^2-6^2}{2*5*4} \right ) =\cos^{-1}\frac{1}{8}$
$\beta =82.82^{\circ \:}$


Now, from angle sum property:
sum of the angle = 180
$\\57.77^{\circ \:} + 82.82^{\circ \:} +\gamma = 180^{\circ \:}\\ \gamma=180^{\circ \:}-140.59^{\circ \:}\\ \gamma = 41.41^{\circ \:}$