1. **Problem statement:** We have a right triangle with a hypotenuse of 105 ft making a 30° angle with the horizontal. The vertical side (height of the tower) is 85 ft, and a man stands on a box of height 27 ft with an unknown height labeled "?". We want to find the man's height. 2. **Step 1: Calculate vertical height from hypotenuse and angle.** The vertical side ($h$) of a right triangle is given by: $$h = 105 \times \sin 30^\circ$$ Since $\sin 30^\circ = 0.5$: $$h = 105 \times 0.5 = 52.5 \text{ ft}$$ 3. **Step 2: Consider the total height as tower height plus man's height on box.** Given total vertical height from hypotenuse angle point is height of tower + height of box + height of man: $$85 = 27 + ? + 52.5$$ Note: This doesn't match geometry. Instead, the vertical height from hypotenuse projection should equal man height + box + tower height. 4. **Step 3: Correct approach:** The triangle with hypotenuse 105 ft and angle 30° forms vertical height $h = 105 \times \sin 30^\circ = 52.5$ ft. Since tower height is 85 ft (vertical), and the hypotenuse height is less than tower, the difference corresponds to man + box height: $$85 = 52.5 + 27 + ?$$ Rearranged: $$? = 85 - 52.5 - 27 = 5.5 \text{ ft}$$ 5. **Step 4: Conclusion:** Man's height is 5.5 ft. **Answer: b) 5.5 ft**