Answer:
∠B = 28°, [tex]a = 69.61\ and\ c = 56.87[/tex]
Step-by-step explanation:
Given:
A triangle ABC with the following data:
∠A = 98°, ∠C = 54°, b = 33
Now, for a triangle, the sum of all interior angles is equal to 180°. So,
∠A + ∠B + ∠C = 180°
⇒ 98° + ∠B + 54° = 180°
⇒ ∠B + 152° = 180°
⇒ ∠B = 180° -152°
⇒ ∠B = 28°
Now, using the sine rule for a triangle, we can find the remaining sides of the triangle. The sine rule is:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\\\\\frac{\sin 98\°}{a}=\frac{\sin 28\°}{33}\\\\a=\frac{33\times \sin 98\°}{\sin 28\°}\\\\a=69.61[/tex]
Now, we consider the second pair of fraction.
[tex]\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]
[tex]\frac{\sin 28\°}{33}=\frac{\sin 54\°}{c}\\\\c=\frac{33\times\sin 54\°}{\sin 28\°}\\\\c=56.87[/tex]
Therefore, the missing data are:
∠B = 28°, a = 69.61 and c = 56.87
