Find the exact value of the given trigonometric function of the angle $\theta$ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
Find: $\sin \theta$

A) $8 \sqrt { 2 }$
B) $\sqrt { 2 }$
C) $\frac { \sqrt { 2 } } { 2 }$
D) 1
E) $\frac { \sqrt { 2 } } { 8 }$

Question

Find the exact value of the given trigonometric function of the angle $\theta$ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
Find: $\sin \theta$

A) $8 \sqrt { 2 }$ 
B) $\sqrt { 2 }$ 
C) $\frac { \sqrt { 2 } } { 2 }$ 
D) 1 
E) $\frac { \sqrt { 2 } } { 8 }$

Quizplus · Accepted Answer

Using the Pythagorean Theorem, we can find that the length of the third side of the triangle is $8$. Then, $\sin	heta=\frac{	ext{opposite}}{	ext{hypotenuse}}=\frac{8}{8\sqrt{2}}=\frac{\sqrt{2}}{2}$. Therefore, the answer is choice $	ext{(C)}$.

Find the Exact Value of the Given Trigonometric Function of the Angle