Refer to the triangle and compute $\sin 2 s$ .
A) $\frac { 120 } { 169 }$
B) $- \frac { 245 } { 389 }$
C) $\frac { 201 } { 389 }$
D) $- \frac { 119 } { 169 }$
E) $- \frac { 119 } { 120 }$

Question

Refer to the triangle and compute $\sin 2 s$ . 
A) $\frac { 120 } { 169 }$ 
B) $- \frac { 245 } { 389 }$ 
C) $\frac { 201 } { 389 }$ 
D) $- \frac { 119 } { 169 }$ 
E) $- \frac { 119 } { 120 }$

Quizplus · Accepted Answer

Using the sine formula, we have:

$$\sin2s=2\sin s \cos s$$

Applying the Pythagorean theorem in the triangle, we have $\cos s = \frac{120}{169}$ and $\sin s = \frac{119}{169}$.

Substituting in the formula we have:

$$\sin2s=2\cdot \frac{119}{169}\cdot \frac{120}{169}=\frac{28560}{28561}=\frac{120^2}{120^2+119^2}$$

Therefore, the answer is A.

Refer to the Triangle and Compute sin⁡2s\sin 2 ssin2s A)

Refer to the Triangle and Compute $\sin 2 s$
A)