the hypotenuse of right triangle abc, line segment ac, measures 13 cm. the length of line segment bc is 5…

Answer:

A. $34.8^{\circ}$

Explanation:

Step1: Find $\sin A$

In right - triangle $ABC$, $\sin A=\frac{BC}{AC}$. Given $AC = 13$ cm and $BC = 5$ cm, so $\sin A=\frac{5}{13}$. Then $m\angle A=\sin^{- 1}(\frac{5}{13})\approx22.6^{\circ}$.

Step2: Find $\sin C$

Since $\sin C=\frac{AB}{AC}$, first find $AB$ using the Pythagorean theorem $AB=\sqrt{AC^{2}-BC^{2}}=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}=12$ cm. So $\sin C=\frac{12}{13}$, and $m\angle C=\sin^{-1}(\frac{12}{13})\approx67.4^{\circ}$.

Step3: Calculate the difference

$m\angle C - m\angle A=67.4^{\circ}-22.6^{\circ}=44.8^{\circ}$.