1. **Problem statement:** The shadow of a skyscraper is 100 m longer when the angle of elevation of the sun is 40° than when it is 60°. We need to find the height of the skyscraper. 2. **Formula and concept:** The length of the shadow $s$ of an object of height $h$ when the sun's angle of elevation is $\theta$ is given by: $$ s = \frac{h}{\tan(\theta)} $$ 3. **Set up equations:** Let $h$ be the height of the skyscraper. - Shadow length at 40°: $s_{40} = \frac{h}{\tan 40^\circ}$ - Shadow length at 60°: $s_{60} = \frac{h}{\tan 60^\circ}$ Given that $s_{40} - s_{60} = 100$ meters. 4. **Write the equation:** $$ \frac{h}{\tan 40^\circ} - \frac{h}{\tan 60^\circ} = 100 $$ 5. **Factor out $h$:** $$ h \left( \frac{1}{\tan 40^\circ} - \frac{1}{\tan 60^\circ} \right) = 100 $$ 6. **Calculate the tangent values:** - $\tan 40^\circ \approx 0.8391$ - $\tan 60^\circ = \sqrt{3} \approx 1.7321$ 7. **Calculate the difference:** $$ \frac{1}{0.8391} - \frac{1}{1.7321} \approx 1.1918 - 0.5774 = 0.6144 $$ 8. **Solve for $h$:** $$ h = \frac{100}{0.6144} \approx 162.66 $$ **Answer:** The height of the skyscraper is approximately **163 meters**.