Question

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

1. 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: Rearrange the Pythagorean formula

Starting with $c = \sqrt{a^{2}+b^{2}}$, we square both sides to get $c^{2}=a^{2}+b^{2}$. Then we solve for $b^{2}$: $b^{2}=c^{2}-a^{2}$.

Step2: Substitute given values

Substitute $c = 50.00$ and $a = 16.00$ into the equation $b^{2}=c^{2}-a^{2}$. So $b^{2}=(50.00)^{2}-(16.00)^{2}=2500 - 256=2244$.

Step3: Solve for b

Take the square - root of both sides. Since $b$ represents a length, we take the positive square root. $b=\sqrt{2244}\approx47.37$ mm.

Answer:

$47.37$ mm