Question

1) g = 23.6, E = 27.6°, G = 123.4°2) g = 24.6, E = 30.6°, G = 116.4°3) g = 25.6, E = 29.6°, G = 111.4°4) none

Answer 1

Given :

f=15

e=14

F=33 degrees

Solution:

Using Sine laws,

a/sin A = b/sin B = c/sin C

Here, a,b,c is the sides

The values are taken,

Let's take the case,

e/sin E = f/sin F = g/ sin G

f/sin F = e/sin E

a) Angle E is obtained,

15/sin 33° =14/sin E

27.5 =14/sin E

sin E= 14/27.50

sin E=0.508

E= sin⁻¹(0.508)

∠E=30.6°

b) Sum of angles in a triangle is 180 degrees. Thus, calculating angle G,

∠G = 180°-(30.6°+33°)

∠G = 180°-(63.6°)

∠G = 116.4°

c) The side g is found out,

g/sinG =f/sinF

g/sin 116.4°=15/sin 33°

g/sin 116.4°=15/0.544

g/116.4° = 27.50

g= 27.50 sin 116.4°

g=24.6