Answer:
5. √119 in
6. √52 in
Step-by-step explanation:
In a right angle triangle, there are two sides (i.e. the legs) between which is the right-angle, and the third side of the triangle joins these two sides and is known as the hypotenuse (P.S. always the longest side);
Pythagoras theorem applies to all right-angle triangles and dictates:
The two sides that have the right-angle between them squared will be equivalent to the hypotenuse squared;
Let:
a = one side adjacent to the right-angle
b = the other side adjacent to the right angle
h = hypotenuse
Then:
a² + b² = h²
Considering we have been provided the hypotenuse and one of the legs:
We can plug these values into this equation and solve for the remaining side:
a² + (5)² = (12)²
a² + 25 = 144
a² = 144 - 25
a² = 119
a = √119
6.
This question is a practical example of the Pythagoras theorem in the real world;
The longest length that will exist within the cylindrical can will be from a point along the bottom circumference of the can diagonally, across the diameter, up to the rim of the can on the opposite side;
This will also be the length of the longest nail, or an item of any kind for that matter, that can fit in the can entirely;
The diameter is 4 in;
The height is 6 in;
These two will be the two legs of a right-angle triangle;
The hypotenuse is the solution we want;
Once again:
a² + b² = h²
(4)² + (6)² = h²
16 + 36 = h²
52 = h²
h = √52
