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 $\mathrm { a } = \sqrt { 13 }$ and $\mathrm { c } = 10$.
A) $\frac { 13 } { 10 }$
B) $\frac { \sqrt { 87 } } { 10 }$
C) $\frac { 87 } { 13 }$
D) $\frac { \sqrt { 13 } } { 10 }$

Question

Quizplus · Accepted Answer

In a right triangle, the cosine of an angle is the adjacent side over the hypotenuse. Here, $\cos A = \frac{b}{c}$. Given $a = \sqrt{13}$ and $c = 10$, we can find $b$ using Pythagoras' theorem: $a^2 + b^2 = c^2$. Substituting the given values, we get $\sqrt{13}^2 + b^2 = 10^2$, which simplifies to $13 + b^2 = 100$. Solving for $b^2$, we find $b^2 = 87$, so $b = \sqrt{87}$. Therefore, $\cos A = \frac{\sqrt{87}}{10}$.

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