The problem provides a diagram of a right-angled triangle with sides x, y, and z.

Step 1: Identify the given information. The problem provides a diagram of a right-angled triangle with sides $x$, $y$, and $z$. It also gives the values of two trigonometric ratios: $\sin \theta = \frac{3}{5}$ $\cos \phi = \frac{12}{13}$

• Step 2: Relate $\sin \theta$ to the sides of the triangle. In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. From the diagram, for angle $\theta$: Opposite side = $y$ Hypoten