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 $\sin \mathrm { A }$ when $\mathrm { a } = 4$ and $\mathrm { b } = 5$.
A) $\frac { \sqrt { 41 } } { 4 }$
B) $\frac { 4 \sqrt { 41 } } { 41 }$
C) $\frac { \sqrt { 41 } } { 5 }$
D) $\frac { 5 \sqrt { 41 } } { 41 }$

Question

Quizplus · Accepted Answer

First, find the hypotenuse $ c $ using the Pythagorean theorem: $ c = \sqrt{a^2 + b^2} = \sqrt{4^2 + 5^2} = \sqrt{41} $. Then, $\sin A = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{4}{\sqrt{41}}$. Rationalizing the denominator gives $\frac{4 \sqrt{41}}{41}$.

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

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