1. **State the problem:** We have a flagpole on top of a building that is 9.0 m tall. From the top of the flagpole, the angle of depression to a spot on the ground is 49°. 2. From the base of the flagpole (which is the top of the building), the angle of depression to the same spot on the ground is 39°. 3. We need to find the height of the building. 4. **Set variables:** Let $h$ be the height of the building, and $d$ be the horizontal distance from the building to the spot on the ground. 5. From the top of the flagpole (height $h + 9$), the angle of depression is 49°, so: $$\tan(49^\circ) = \frac{h + 9}{d}$$ 6. From the base of the flagpole (height $h$), the angle of depression is 39°, so: $$\tan(39^\circ) = \frac{h}{d}$$ 7. From step 5 and 6, express $d$: $$d = \frac{h + 9}{\tan(49^\circ)} = \frac{h}{\tan(39^\circ)}$$ 8. Set the two expressions for $d$ equal: $$\frac{h + 9}{\tan(49^\circ)} = \frac{h}{\tan(39^\circ)}$$ 9. Cross multiply: $$h \times \tan(49^\circ) = (h + 9) \times \tan(39^\circ)$$ 10. Expand right side: $$h \tan(49^\circ) = h \tan(39^\circ) + 9 \tan(39^\circ)$$ 11. Rearrange terms to isolate $h$: $$h \tan(49^\circ) - h \tan(39^\circ) = 9 \tan(39^\circ)$$ 12. Factor out $h$: $$h (\tan(49^\circ) - \tan(39^\circ)) = 9 \tan(39^\circ)$$ 13. Solve for $h$: $$h = \frac{9 \tan(39^\circ)}{\tan(49^\circ) - \tan(39^\circ)}$$ 14. Calculate values: $$\tan(39^\circ) \approx 0.8098$$ $$\tan(49^\circ) \approx 1.1504$$ 15. Substitute: $$h = \frac{9 \times 0.8098}{1.1504 - 0.8098} = \frac{7.2882}{0.3406} \approx 21.41$$ 16. **Final answer:** The height of the building is approximately **21.41 meters**.