1. **State the problem:** We have a tent shaped like an isosceles triangular prism. We need to find the length $a$ of the segment from the top front corner to the front bottom right corner, and then use $a$ to find the length $b$ of the pole from the top front corner to the back bottom right corner. 2. **Given dimensions:** The vertical height is 12 ft, the base segment is 9 ft, and the side length of the triangular base is 17 ft. 3. **Find $a$:** The segment $a$ forms a right triangle with the vertical height (12 ft) and the base segment (9 ft). Use the Pythagorean theorem: $$a = \sqrt{12^2 + 9^2}$$ Calculate: $$a = \sqrt{144 + 81} = \sqrt{225} = 15$$ So, $a = 15$ ft. 4. **Find $b$:** The pole $b$ forms a right triangle with $a$ (15 ft) and the side length of the base (17 ft). Use the Pythagorean theorem again: $$b = \sqrt{a^2 + 17^2} = \sqrt{15^2 + 17^2}$$ Calculate: $$b = \sqrt{225 + 289} = \sqrt{514} \approx 22.7$$ So, $b \approx 22.7$ ft. **Final answers:** - $a = 15$ ft - $b \approx 22.7$ ft