Answer:
[tex]a=\sqrt{609}\\\\a\approx 24.67793[/tex]
Step-by-step explanation:
To solve for the leg of the missing right triangle, one must use the Pythagorean theorem. The Pythagorean theorem states the following,
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the sides adjacent to or next to the right angle. (c) is the side opposite the right angle. Substitute in the given values and solve for the unknown,
[tex]a^2+b^2=c^2\\[/tex]
Substitute,
[tex]a^2+40^2=47^2\\[/tex]
Simplify,
[tex]a^2+1600=2209\\[/tex]
Inverse operations,
[tex]a^2=609[/tex]
[tex]a=\sqrt{609}\\\\a\approx 24.67793[/tex]
