Using the Pythagorean Theorem with the given sides of 35 mm and 84 mm, the length of the hypotenuse is calculated to be 91 mm.
Calculating the Hypotenuse
To determine the length of the unknown side of a right-angled triangle, the Pythagorean Theorem can be used. This theorem states that in a right-angled 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 situation, we have two known sides, 35 mm and 84 mm, which can be considered as the two shorter sides of the triangle, known as the legs.
To find the length of the hypotenuse, you use the formula:
c2 = a2 + b2
where 'c' represents the length of the hypotenuse and 'a' and 'b' represent the lengths of the other two sides.
Substituting our known values into this formula we get:
c2 = 352 + 842
c2 = 1225 + 7056
c2 = 8281
By taking the square root of both sides, we obtain the length of the hypotenuse:
c = √8281
c = 91
Therefore, the length of the unknown side, the hypotenuse, is 91 mm.
The probable question may be:
In a crafting workshop, a right-angled triangle is being used to create a decorative corner piece. The known sides of the triangle are represented as follows: one side is 35 mm long, the other side is 84 mm long.
The length of the unknown side is mm.
Additional Information:
Imagine you are creating a beautiful corner accent for a scrapbooking project. The side lengths of 35 mm and 84 mm represent the edges of the right-angled triangle that forms a charming corner detail. You're keen to know the length of the unknown side to ensure your crafting project is precise.