1. **State the problem:** We have a right triangle with hypotenuse $R=5$ and need to find the value of $r$, the trigonometric ratios $\sin(\theta)$, $\cos(\theta)$, $\tan(\theta)$, and the angle measure $\theta$. We also need to plot the point and draw the triangle with labels. 2. **Plot the point and draw the triangle:** Since the problem mentions a right triangle and $R=5$, assume the hypotenuse is 5 units. We place the point at $(r, y)$ on the coordinate grid such that the triangle is right angled. 3. **Calculate $r$:** Using the Pythagorean theorem for a right triangle, $$R^2 = r^2 + y^2$$ Given $R=5$, if $y$ is known or can be inferred, solve for $r$: $$r = \sqrt{R^2 - y^2} = \sqrt{25 - y^2}$$ 4. **Determine trigonometric ratios:** - $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{y}{5}$ - $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{r}{5}$ - $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{y}{r}$ 5. **Calculate angle $\theta$:** Use inverse trigonometric functions, for example, $$\theta = \arcsin\left(\frac{y}{5}\right)$$ Since the exact $y$ or $r$ values are not provided, the formulas above show how to calculate each quantity once those values are known. **Final answers depend on the specific coordinates of the point and the triangle sides, which must be given or measured from the graph.**