Question

1. these formulas have been taken from various technical fields. substitute the given values for letter values and solve for the unknown. check each answer

this is the formula for finding the hypotenuse of a right triangle. round the answer to 4 significant digits.
c = \\( \sqrt { a ^ { 2 } + b ^ { 2 } } \\) where c = hypotenuse
a = first side
b = second side
solve for b when c = 50.00 mm and a = 16.00 mm

Explanation:

Step1: Substitute the values into the formula

Given \(c = 50.00\) and \(a=16.00\), substitute into \(c=\sqrt{a^{2}+b^{2}}\). First, square both sides of the equation to get \(c^{2}=a^{2}+b^{2}\). Then, solve for \(b^{2}\): \(b^{2}=c^{2}-a^{2}\). Substituting the values: \(b^{2}=(50.00)^{2}-(16.00)^{2}\).

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Step2: Solve for \(b\)

Take the square root of \(b^{2}\) to find \(b\). \(b=\sqrt{2244}\approx47.37\) (rounded to 4 significant digits)

Step3: Check the answer

Substitute \(a = 16.00\), \(b\approx47.37\) into the original formula \(c=\sqrt{a^{2}+b^{2}}\)

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Answer:

\(b\approx47.37\) mm