1. **State the problem:** Determine the type of triangle based on the side lengths and verify if it is right, acute, or obtuse. 2. **Recall the Pythagorean theorem:** For a triangle with sides $a$, $b$, and hypotenuse $c$, if $a^2 + b^2 = c^2$, the triangle is right-angled. 3. **Check the first triangle:** Given sides 8, 15, and 17. Calculate $8^2 + 15^2 = 64 + 225 = 289$. Calculate $17^2 = 289$. Since $64 + 225 = 289$, the triangle is right-angled, not obtuse. 4. **Check the second triangle:** Given sides 3, $\sqrt{34}$, and 13. Calculate $3^2 + (\sqrt{34})^2 = 9 + 34 = 43$. Calculate $13^2 = 169$. Since $43 \neq 169$ and $43 < 169$, the triangle is acute, not obtuse. 5. **Summary:** The first triangle with sides 8, 15, 17 is right-angled. The second triangle with sides 3, $\sqrt{34}$, 13 is acute. 6. **Regarding the graph description:** Triangle ABC with right angle at D on AB, sides AC=13, BC=15, CD=2, AD=12 confirms the right angle at D. Final answer: The first triangle is right-angled, the second is acute.