Answer: Angle A = 15.42°, angle B = 147.58°, and side b = 20.17 units.
Step-by-step explanation: Please refer to the attached diagram for details.
A triangle with angles ABC has been sketched from the information given, and we have the missing dimensions as, angles A and B and side b. Since we have an angle with a corresponding side, and another side has been given, we shall apply the Sine Rule which states that;
a/SinA = b/SinB = c/SinC
We can start with the known values as follows
a/SinA = c/SinC
10/SinA = 11/Sin 17
By cross multiplication we now have
(10 x Sin 17)/11 = SinA
(10 x 0.2924)/11 = SinA
2.924/11 = SinA
0.2658 = SinA
By use of calculator or a table of values,
A = 15.42°
Having calculated angle A as 15.42 and having known angle C as 17, angle B can be derived as,
A + B + C = 180° {Sum of angles in a triangle equals 180}
15.42 + B + 17 = 180
32.42 + B = 180
Subtract 32.42 from both sides of the equation
B = 147.58°
And now to calculate the missing side c, we still apply the Sine Rule
b/SinB = c/SinC
b = (c x SinB)/SinC
b = (11 x 0.5361)/0.2924
b = 5.8971/0.2924
b = 20.168
Approximately, b = 20.17
Therefore, the missing angles and side is calculated as
Angle A = 15.42°, angle B = 147.58° and length of side b = 20.17 units
