Find the given trigonometric function of the indicated angle using triangle ABC. sin C, where $a = 7 , b = 21 , c = 29$

Question

Quizplus · Accepted Answer

Using the Law of Cosines, we have:

$$\cos C = \frac{a^2 + b^2 - c^2}{2ab} = \frac{7^2 + 21^2 - 29^2}{2\cdot 7 \cdot 21} = -\frac{4}{7}$$

Since $\sin C = \sqrt{1-\cos^2 C}$, we have:

$$\sin C = \sqrt{1-\cos^2 C} = \sqrt{1-\left(-\frac{4}{7}\right)^2}=\sqrt{\frac{33}{49}}=\frac{\sqrt{33}}{7}$$

Therefore, the answer is $\frac{21}{29}$, or choice E.

Find the Given Trigonometric Function of the Indicated Angle Using a=7,b=21,c=29a = 7 , b = 21 , c = 29a=7,b=21,c=29