Question

I'm not sure where to begin

Answer 1

Answer:

∠B = 28°, $a = 69.61\ and\ c = 56.87$

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:

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\\\\\frac{\sin 98\°}{a}=\frac{\sin 28\°}{33}\\\\a=\frac{33\times \sin 98\°}{\sin 28\°}\\\\a=69.61$

Now, we consider the second pair of fraction.

$\frac{\sin B}{b}=\frac{\sin C}{c}$

$\frac{\sin 28\°}{33}=\frac{\sin 54\°}{c}\\\\c=\frac{33\times\sin 54\°}{\sin 28\°}\\\\c=56.87$

Therefore, the missing data are:

∠B = 28°, a = 69.61 and c = 56.87