Answer:
10.97 mm
Step-by-step explanation:
Hello!
First, let's construct an altitude, as shown in the picture below. An altitude is a height from one point to another side, forming a 90° angle at that intersection.
The length of the altitude is the same as the missing length, they are both parallel.
The length from the altitude to the slant line would be 6, as found by subtracting 8 from 14.
If you look closely, we can see a right triangle, and 12.5 mm is the hypotenuse. We know the measure for another side, and we can solve for the altitude using the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex], a and b are legs, and c is the hypotenuse.
In this case, 6 and the altitude are legs.
Solve for the Altitude
- [tex]a^2 + b^2 = c^2[/tex]
- [tex]A^2 + 6^2 = 12.5^2[/tex]
- [tex]A^2 + 36 = 156.25[/tex]
- [tex]A^2 = 120.25[/tex]
- [tex]A = \sqrt{120.25}[/tex]
- [tex]A \approx 10.97[/tex]
The altitude is around 10.97, so the missing length will also be 10.97 mm.
