Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.
-Find $\cos \mathrm { A }$ when $\mathrm { a } = 3$ and $\mathrm { b } = 7$.
A) $\frac { \sqrt { 58 } } { 7 }$
B) $\frac { 7 \sqrt { 58 } } { 58 }$
C) $\frac { 3 \sqrt { 58 } } { 58 }$
D) $\frac { \sqrt { 58 } } { 3 }$

Question

Quizplus · Accepted Answer

In a right triangle, $\cos A = \frac{b}{c}$, where $c$ is the hypotenuse. Using the Pythagorean theorem, $c = \sqrt{a^2 + b^2} = \sqrt{3^2 + 7^2} = \sqrt{58}$. Thus, $\cos A = \frac{7}{\sqrt{58}}$, which rationalizes to $\frac{7\sqrt{58}}{58}$.

Two Sides of a Right Triangle ABC (C Is the Right