1. **State the problem:** We have a right triangle SRQ with a right angle at R. Side SR = 35, angle Q = 40°, and we need to find side SQ = x. 2. **Identify the sides relative to angle Q:** - SR is adjacent to angle Q. - SQ is the hypotenuse. 3. **Use the cosine function:** $$\cos(\text{angle Q}) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{SR}{SQ} = \frac{35}{x}$$ 4. **Set up the equation:** $$\cos(40^\circ) = \frac{35}{x}$$ 5. **Solve for x:** Multiply both sides by x: $$x \cos(40^\circ) = 35$$ Divide both sides by \cos(40^\circ): $$x = \frac{35}{\cos(40^\circ)}$$ 6. **Calculate the value:** $$x = \frac{35}{\cos(40^\circ)} = \frac{35}{0.7660} \approx 45.7$$ **Final answer:** $$x \approx 45.7$$