Answer:
See below ↓
Step-by-step explanation:
Finding w and x [both are equal]
- Take the cos function of one of the 45° angles, which is the ratio of the adjacent side to the hypotenuse
- cos(45°) = [tex]\frac{1}{\sqrt{2} } = \frac{w}{6}[/tex]
- ⇒ w = [tex]\frac{6}{\sqrt{2} } = \frac{6}{\sqrt{2} } *\frac{\sqrt{2} }{\sqrt{2} } = \frac{6\sqrt{2} }{2}[/tex]
- ⇒ w = 3√2 and x = 3√2
Finding y
- Take the cos ratio of the 60° angle to find y
- cos(60°) = [tex]\frac{1}{2} = \frac{y}{x} = \frac{y}{3\sqrt{2} }[/tex]
- ⇒ y = [tex]\frac{3\sqrt{2} }{2}[/tex]
Finding z
- Take the sin ratio of 60° angle of the triangle, which is the ratio of the opposite side to the hypotenuse
- sin(60°) = [tex]\frac{\sqrt{3} }{2}= \frac{z}{x} = \frac{z}{3\sqrt{2} }[/tex]
- ⇒ z = [tex]\frac{3\sqrt{6} }{2}[/tex]
