1. **Problem statement:** We have two buildings on level ground, 10 m apart. From the top of the first building, the angle of elevation to the top of the skyscraper is 70° and the angle of depression to the base of the skyscraper is 30°. We need to find the height of the skyscraper. 2. **Setup and notation:** Let the height of the first building be $h_1$ and the height of the skyscraper be $h_2$. The horizontal distance between the buildings is $d = 10$ m. 3. **Using the angle of depression:** The angle of depression from the top of the first building to the base of the skyscraper is 30°. This means the line of sight from the top of the first building to the base of the skyscraper makes a 30° angle below the horizontal. 4. **Using the angle of elevation:** The angle of elevation from the top of the first building to the top of the skyscraper is 70°. This means the line of sight from the top of the first building to the top of the skyscraper makes a 70° angle above the horizontal. 5. **Relate heights and distances:** Draw a horizontal line from the top of the first building. The vertical drop to the base of the skyscraper forms a right triangle with angle 30° and horizontal side 10 m. The vertical height difference from the top of the first building down to the base of the skyscraper is: $$h_1 = d \tan 30^\circ = 10 \times \tan 30^\circ$$ 6. **Calculate $h_1$:** $$h_1 = 10 \times \frac{1}{\sqrt{3}} = \frac{10}{\sqrt{3}} \approx 5.77 \text{ m}$$ 7. **Height difference between tops:** The angle of elevation to the top of the skyscraper is 70°, so the vertical height difference between the tops is: $$h_2 - h_1 = d \tan 70^\circ = 10 \times \tan 70^\circ$$ 8. **Calculate $h_2 - h_1$:** $$h_2 - h_1 = 10 \times 2.747 = 27.47 \text{ m}$$ 9. **Calculate $h_2$:** $$h_2 = h_1 + (h_2 - h_1) = 5.77 + 27.47 = 33.24 \text{ m}$$ **Final answer:** The height of the skyscraper is approximately **33.24 m**.