Answer:
see explanation
Step-by-step explanation:
Since the triangles are right use trigonometric ratios to find x and y
A
sin33° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2.5}x}[/tex]
Multiply both sides by x
x × sin33° = 2.5 ( divide both sides by sin33° )
x = [tex]\frac{2.5}{sin33}[/tex] ≈ 4.590
tan33° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{2.5}{y}[/tex]
Multiply both sides by y
y × tan33° = 2.5 ( divide both sides by tan33° )
y = [tex]\frac{2.5}{tan33}[/tex] ≈ 3.850
B
cos72° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex]
Multiply both sides by x
x × cos72° = 6 ( divide both sides by cos72° )
x = [tex]\frac{6}{cos72}[/tex] ≈ 19.416
tan72° = [tex]\frac{y}{6}[/tex]
Multiply both sides by 6
6 × tan72° = y, thus
y ≈ 18.466
