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You have prizeEighth grade T.1 Pythagorean theorem: find the length of the hypotenuse 7Z
42 km
56 km
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
kilometerS.

Answer 1

The length of the hypotenuse, calculated using the Pythagorean theorem for a right-angled triangle with legs measuring 42 km and 56 km, is approximately 70.9 km when rounded to the nearest tenth.

Step-by-step explanation:

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (\(c\)) is equal to the sum of the squares of the lengths of the other two sides (\(a\) and \(b\)). The formula is given by:

`\[c^2 = a^2 + b^2\]`

In this scenario, the lengths of the legs are \(a = 42 \, \text{km}\) and \(b = 56 \, \text{km}\). Substituting these values into the Pythagorean theorem:

`\[c^2 = 42^2 + 56^2\]`

Calculating the squares and sum:

`\[c^2 = 1764 + 3136\]`

`\[c^2 = 4900\]`

Now, to find \(c\), take the square root of both sides:

`\[c = √(4900) = 70\, \text{km}\]`

Rounding to the nearest tenth gives approximately \(70.9 \, \text{km}\) as the final answer for the length of the hypotenuse. Therefore, in a right-angled triangle with legs measuring 42 km and 56 km, the length of the hypotenuse is approximately 70.9 km. Understanding and applying the Pythagorean theorem is essential for solving problems involving right-angled triangles and calculating distances in various real-world situations.