Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 angles from 180° for B
B = 180° - (90 + 47)° = 180° - 137° = 43°
Use the tangent and cosine ratios in the right triangle for a and c
tan47° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{a}{18}[/tex]
Multiply both sides by 18
18 × tan47° = a , thus
a ≈ 19.3 ( to the nearest tenth )
cos47° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{18}{c}[/tex]
Multiply both sides by c
c × cos47° = 18 ( divide both sides by cos47° )
c = [tex]\frac{18}{cos47}[/tex] ≈ 26.4 ( to the nearest tenth )
