Question

question 10 (multiple choice worth 1 points)
(triangle trigonometry lc)
the legs of a right triangle measure 14.6 m and 9.2 m. what is the length of the hypotenuse?
17.3 m
11.3 m
23.8 m
6.9 m

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 14.6\) and \(b=9.2\), and hypotenuse \(c\), the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 14.6\) and \(b = 9.2\) into the formula: \(c=\sqrt{(14.6)^{2}+(9.2)^{2}}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\((14.6)^{2}=14.6\times14.6 = 213.16\), \((9.2)^{2}=9.2\times9.2=84.64\).
Then \(a^{2}+b^{2}=213.16 + 84.64=297.8\).

Step3: Calculate the square root

\(c=\sqrt{297.8}\approx17.3\) (using a calculator to find \(\sqrt{297.8}\)).

Answer:

17.3 m