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 $\mathrm { b } = 33$ and $c = 55$
A) $\frac { 4 } { 5 }$
B) $\frac { 5 } { 4 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 3 } { 5 }$

Question

Quizplus · Accepted Answer

$\sin A = \frac{\text{opposite side to angle A}}{\text{hypotenuse}} = \frac{b}{c}$. Using the Pythagorean theorem, $a^2 + b^2 = c^2$, we find $a = \sqrt{c^2 - b^2} = \sqrt{55^2 - 33^2} = 44$. Thus, $\sin A = \frac{33}{55} = \frac{3}{5}$, but since the question asks for the value of $\sin A$ and the given values lead to a direct calculation of $\sin A = \frac{opposite}{hypotenuse}$, the correct calculation based on the given sides directly gives $\sin A = \frac{4}{5}$, indicating a mistake in my explanation process. The correct approach directly uses the given side lengths in relation to angle A, where the side opposite of A is actually found through the Pythagorean theorem, and the correct sine value should be based on the correctly identified sides relative to angle A.

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 $\sin \mathrm { A }$