Answer:
72 units
Step-by-step explanation:
The Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex] in a right triangle when a and b are the two legs and c is the hypotenuse (the longest side).
[tex]a^2+b^2=c^2[/tex]
In the diagram, 30 measures one of the legs and 78 measures the hypotenuse. Plug these in as a and c.
[tex]30^2+b^2=78^2\\900+b^2=6084[/tex]
Subtract 900 from both sides
[tex]900+b^2-900=6084-900\\b^2=5184[/tex]
Take the square root of both sides
[tex]900+b^2-900=6084-900\\\sqrt{b^2} =\sqrt{5184}\\b=72[/tex]
Therefore, the length of the missing side is 72 units.
I hope this helps!
