Answer: The length of ¯¯¯¯NP is 10 inches.
Explanation:
To find the length of ¯¯¯¯NP, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, triangle NOP is a right triangle because angle N is a right angle (shown by the small square in the corner). Therefore, we can use the Pythagorean theorem to find the length of ¯¯¯¯NP.
Let's label the sides of triangle NOP. The side opposite angle N is ¯¯¯¯OP, which has a length of 8 inches. The side opposite angle P is ¯¯¯¯NO, which has a length of 6 inches. Finally, the hypotenuse, which we want to find, is ¯¯¯¯NP.
Using the Pythagorean theorem, we get:
¯¯¯¯NP2=¯¯¯¯OP2+¯¯¯¯NO2
¯¯¯¯NP2=82+62
¯¯¯¯NP2=64+36
¯¯¯¯NP2=100
Therefore,
¯¯¯¯NP=sqrt(100)=10