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 have:

$$9^2 + 9^2 = c^2$$
$$81 + 81 = c^2$$
$$162 = c^2$$
$$c = \sqrt{162} = 9\sqrt{2}$$

Now, we can use the definition of sine to find $\sin \theta$:

$$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{9}{9\sqrt{2}} = \frac{\sqrt{2}}{2}$$

Therefore, the best choice is C.

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