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Sagot :

sreedevi102

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]

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