Answer:
m ∠B = 69°
b = 36.5
c= 39.1
Step-by-step explanation:
Sum of angles in a triangle is 180°. Therefore,
[tex]\angle A + \angle B + \angle C = 180^\circ\\\\21^ \circ + \angle B + 90 ^\circ = 180^\circ\\\\ \angle B = 180^\circ - 21^ \circ - 90^ \circ\\\\\angle B = 69^ \circ[/tex]
Now using trigonometric ratios :
[tex]Sin A = \frac{opposite}{hypotenuse}=\frac{BC}{AB} \\\\Sin A= \frac{a}{c}\\\\Sin 21 = \frac{14}{c}\\\\c= \frac{14}{sin 21} = 39.1[/tex]
Again we will use Pythagoras theorem:
[tex]c^2 = a^2 + b^2\\39.1^2 = 14^2 + b^2\\b^2 = 1332.81\\b= \sqrt{1332.81}\\b=36.5[/tex]
