QuestionIn right triangle ABC, with sides a=7 and c=10, find side b using the Pythagorean theorem and calculate sin, cos, tan, csc, sec, cot for angle B.

Studdy Solution
Rationalize the denominators of the trigonometric functions where applicable. This involves multiplying the numerator and denominator by the conjugate of the denominator$$\tan B = \frac{7\sqrt{51}}{51}$$$$\sec B = \frac{\sqrt{51}}{51}$$$$\cot B = \frac{7\sqrt{51}}{49}$$So, the six trigonometric functions for angle B are$$\sin B = \frac{7}{}, \cos B = \frac{\sqrt{51}}{}, \tan B = \frac{7\sqrt{51}}{51}$$$$\csc B = \frac{}{7}, \sec B = \frac{\sqrt{51}}{51}, \cot B = \frac{7\sqrt{51}}{49}$$