Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using
the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize
the denominator if applicable.
-Find $\cos \mathrm { A }$ when $\mathrm { a } = \sqrt { 7 }$ and $\mathrm { c } = 6$.
A) $\frac { 7 } { 6 }$
B) $\frac { 29 } { 7 }$
C) $\frac { \sqrt { 29 } } { 6 }$
D) $\frac { \sqrt { 7 } } { 6 }$

Question

Quizplus · Accepted Answer

The Pythagorean theorem states that $a^2 + b^2 = c^2$. Given $a = \sqrt{7}$ and $c = 6$, we can find $b$ by substituting the given values into the theorem: $(\sqrt{7})^2 + b^2 = 6^2$, which simplifies to $7 + b^2 = 36$. Solving for $b^2$ gives $b^2 = 29$, so $b = \sqrt{29}$. The cosine of angle A, $\cos(A)$, is adjacent over hypotenuse, which is $\frac{\sqrt{29}}{6}$.

Suppose ABC Is a Right Triangle with Sides of Lengths cos⁡A\cos \mathrm { A }cosA

Suppose ABC Is a Right Triangle with Sides of Lengths $\cos \mathrm { A }$