Use the formula and given information to solve for the indicated variable. Round answers to two decimal places as necessary.
[tex]C=\sqrt{a^2+b^2}[/tex]
Given: [tex]a =24[/tex] and [tex]b =13[/tex]
Calculate C.
Answer (2)
Substitute the given values into the formula: C = 2 4 2 + 1 3 2 .
Calculate the squares: 2 4 2 = 576 and 1 3 2 = 169 .
Add the squares: 576 + 169 = 745 .
Take the square root and round to two decimal places: C = 745 ≈ 27.29 .
Explanation
Understanding the Problem We are given the formula C = a 2 + b 2 and the values a = 24 and b = 13 . Our goal is to calculate the value of C .
Substituting the Values First, we substitute the given values of a and b into the formula: C = 2 4 2 + 1 3 2
Calculating the Squares Next, we calculate 2 4 2 and 1 3 2 :
2 4 2 = 576 1 3 2 = 169
Adding the Squares Now, we add the results: 576 + 169 = 745
Finding the Square Root Then, we take the square root of the sum: C = 745 C ≈ 27.294688127912362
Rounding the Result Finally, we round the result to two decimal places: C ≈ 27.29
Final Answer Therefore, the value of C is approximately 27.29.
Examples
The Pythagorean theorem, C = a 2 + b 2 , is used in construction to ensure that corners are square. For example, if a builder wants to make sure a wall is perfectly square, they can measure 24 inches along one wall and 13 inches along the other. The diagonal distance should then be approximately 27.29 inches to ensure a right angle.
By substituting the values a = 24 and b = 13 into the formula C = a 2 + b 2 , we find that the value of C is approximately 27.29 after calculation. This includes squaring the values of a and b, adding them, and taking the square root. The final result is rounded to two decimal places.
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