Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for B
B = 180° - (90 + 39)° = 180° - 129° = 51°
Using the tangent and sine ratios in the right triangle for b and c
tan39° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{27}{b}[/tex]
Multiply both sides by b
b × tan39° = 27 ( divide both sides by tan39° )
b = [tex]\frac{27}{tan39}[/tex] ≈ 7.5 ( to the nearest tenth )
sin39° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{27}{c}[/tex]
Multiply both sides by c
c × sin39° = 27 ( divide both sides by sin39° )
c = [tex]\frac{27}{sin39}[/tex] ≈ 28.0 ( to the nearest tenth )
