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What is the length of the hypotenuse of the triangle? | | | | | --- | --- | --- | | 7 cm | | | | B | 3 cm | C | | | | | | 7 | 20 cm | | | 0 | √23 cm | | | 0 | √40 cm | | | 0 | √58 cm | |
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Answer

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Step 1:
: Identify the given side lengths.

In the given triangle, we are provided with the lengths of two sides, 7 cm (labeled as the side adjacent to angle B) and 3 cm (labeled as the side opposite to angle B). We are asked to find the length of the hypotenuse (labeled as side c).

Step 2:
: Apply the Pythagorean theorem.

c^2 = a^2 + b^2
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (side c) is equal to the sum of the squares of the lengths of the other two sides (sides a and b). In equation form, this can be written as:

Step 3:
: Plug in the known side lengths.

c^2 = (7 \text{ cm})^2 + (3 \text{ cm})^2
Using the given side lengths, we can write:

Step 4:
: Calculate the squares of the side lengths.

c^2 = 49 \text{ cm}^2 + 9 \text{ cm}^2

Step 5:
: Add the squared side lengths.

c^2 = 58 \text{ cm}^2

Step 6:
: Find the square root of both sides.

c = \sqrt{58 \text{ cm}^2}
To find the length of the hypotenuse, we need to take the square root of both sides of the equation:

Step 7:
: Calculate the square root.

c \approx 7.62 \text{ cm}

Final Answer

The length of the hypotenuse is approximately 7.62 cm.