Answer
$$BC=28$$
$$\sin \theta = \frac{4}{5}, \qquad \csc \theta = \frac{5}{4}, \\ \cos \theta = \frac{3}{5}, \qquad \sec \theta = \frac{5}{3}, \\ \tan \theta = \frac{4}{3}, \qquad \cot \theta = \frac{3}{4}.$$
Work Step by Step
Given $AB=35$, and $AC=21$, we can find $BC$ by applying the Pythagorean Theorem as follows.$$BC=\sqrt{(AB)^2-(AC)^2}=\sqrt{35^2-21^2}=28.$$Now, we can find the value of the trigonometric functions easily:$$\sin \theta =\frac{BC}{AB}=\frac{28}{35}=\frac{4}{5}, \quad \csc \theta = \frac{AB}{BC}=\frac{35}{28}=\frac{5}{4} \\ \cos \theta = \frac{AC}{AB}=\frac{21}{35}=\frac{3}{5}, \quad \sec \theta = \frac{AB}{AC}= \frac{35}{21}=\frac{5}{3} \\ \tan \theta = \frac{BC}{AC}=\frac{28}{21}= \frac{4}{3}, \quad \cot \theta = \frac{AC}{BC}=\frac{21}{28}= \frac{3}{4}$$
