Question

question 14
1 pts
in a right triangle, a and b represent legs and c represents the hypotenuse. determine the measure of side c if a = 28.2 cm and b = 12.8 cm. express the answer to the nearest tenth centimeter.
32.0 cm
31.0 cm
25.0 cm
30.0 cm

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\). Given \(a = 28.2\) cm and \(b=12.8\) cm, we substitute these values into the formula: \(c^{2}=(28.2)^{2}+(12.8)^{2}\).
Calculate \((28.2)^{2}=28.2\times28.2 = 795.24\) and \((12.8)^{2}=12.8\times12.8 = 163.84\). Then \(c^{2}=795.24 + 163.84\).

Step2: Calculate \(c^{2}\)

\(c^{2}=795.24+163.84=959.08\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{959.08}\). Using a calculator, \(\sqrt{959.08}\approx30.97\).

Step4: Round to the nearest tenth

Rounding \(30.97\) to the nearest tenth, we look at the hundredth digit. Since \(7\gt5\), we round up. So \(c\approx31.0\) cm.

Answer:

\(31.0\) cm (the second option)