Answer:
Step-by-step explanation:
12). By applying Pythagoras theorem in the given right triangle,
Hypotenuse² = (Leg 1)² + (Leg 2)²
x² = 7² + 7²
x² = 2(7)²
x = [tex]\sqrt{2(7)^{2} }[/tex]
x = [tex]7\sqrt{2}[/tex]
13). By sine rule,
sin(60)° = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{9\sqrt{3} }{y}[/tex]
y = [tex]\frac{18\sqrt{3} }{\sqrt{3} }[/tex]
y = 18
By cosine rule,
cos(60)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{2}=\frac{x}{y}[/tex]
x = [tex]\frac{y}{2}[/tex]
x = [tex]\frac{18}{2}=9[/tex]
14). By applying Pythagoras theorem in the given right triangle,
12² = x² + x²
144 = 2x²
72 = x²
x = √72
x = 6√2
