Solve the triangle using the standard notation a Right trian

Solve the triangle using the standard notation a) Right triangle, = 20°, b = 10 b) Right triangle, a = 5, c = 20 c) = 30°, = 75°, c = 40 d) =3 radians , a=42 , b=14 e) a = 10, b = 20, c = 12

Solution

a) let a be hypotenuse

asin20 = 10 => a = 29.238

acos20 = c => c = 27.475

= 90° , gamma = 70°

b) let = 90

bsin = a

bcos = c

=> tan = 1/4 => = 14.036°

=> gamma = 75.964°

=> b = 5/sin14.036 = 20.616

c)

= 30°, = 75°, c = 40

gamma = 75°   

b =c = 40

a = bsin30/sin75 = 20.705

d)  

=/3 , a=42 , b=14

sin = bsin(/3)/a => = 16.78 degree

gamma = 103.22 degree

c = 42sin(103.22)/sin60 = 47.21

e)   a = 10, b = 20, c = 12

10sin = 20sin => sin = 2sin

12sin = 20sin(gamma)

10sin(gamma) = 12sin