1. **State the problem:** We have a right triangle with hypotenuse 105 ft and an angle of 30° between the ground and the hypotenuse. 2. The tower height is 85 ft, and the stack height is 27 ft. We need to find the height of the person standing on the stack such that the total height equals the vertical leg of the triangle. 3. Use trigonometry: The vertical leg (height from ground to tower top) is given by $$\text{vertical leg} = 105 \times \sin(30^\circ)$$ 4. Calculate $$\sin(30^\circ) = 0.5$$ $$\Rightarrow \text{vertical leg} = 105 \times 0.5 = 52.5 \text{ ft}$$ 5. The tower height plus the stack and person height should sum to this vertical leg. We know tower + stack + person height = vertical leg $$85 + 27 + x = 52.5$$ 6. Sum tower and stack: $$85 + 27 = 112$$ 7. Solve for person height x: $$112 + x = 52.5 \Rightarrow x = 52.5 - 112 = -59.5$$ which is impossible. 8. This means the initial interpretation is incorrect—we must consider that the angle is between the ground and the hypotenuse from the person's eye level (at the top of the stack) to the tower top. 9. The height difference between the tower top and the stack top is $$85 - 27 = 58 \text{ ft}$$ 10. Let the unknown person height be $$h$$ ft. Then, the vertical leg from the person's eye level is $$58 - h$$ ft. 11. The hypotenuse is 105 ft, angle is 30°, so vertical leg from person's eye level is $$105 \times \sin(30^\circ) = 52.5$$ ft. 12. Set the vertical leg equal to the height difference minus person height: $$58 - h = 52.5$$ 13. Solve for $$h$$: $$h = 58 - 52.5 = 5.5 \text{ ft}$$ 14. Therefore, the person’s height is 5.5 ft. **Final answer:** b) 5.5 ft