Answer:
[tex]d=\sqrt{3}[/tex]
[tex]h=7\sqrt{2}[/tex]
Step-by-step explanation:
Use the 45°-45°-90° and 30°-60°-90° rules for right triangles:
45°-45°-90°
[tex]hypotenuse=\sqrt{2}*leg[/tex]
30°-60°-90°
[tex]longer.leg=\sqrt{3}*shorter.leg[/tex]
Solve for the first triangle: Insert values into the equation
[tex]3=\sqrt{3}*d[/tex]
Solve for d: Divide both sides by [tex]\sqrt{3}[/tex]
[tex]\frac{3}{\sqrt{3} }=\frac{\sqrt{3} }{\sqrt{3} } *d\\\\\frac{3}{\sqrt{3} }=d[/tex]
Rationalize and simplify
[tex]\frac{\sqrt{3} }{\sqrt{3} } *\frac{3}{\sqrt{3} }=d\\ \\\frac{3\sqrt{3} }{\sqrt{3}\sqrt{3} } =d\\\\\frac{3\sqrt{3} }{\sqrt{9} }=d\\\\\frac{3\sqrt{3} }{3}=d\\\\\sqrt{3}=d[/tex]
Solve for second triangle: Insert values into the equation
[tex]h=\sqrt{2}*7[/tex]
Simplify
[tex]h=7\sqrt{2}[/tex]
Done.
