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Height of the Empire State Building = h Initial distance of Lil from the building = d1 Initial angle of elevation of the spire atop the building = theta1 = 21o From the figure, \operatorname{Tan} \theta_{1}=\frac{h}{d_{1}} d_{1}=\frac{h}{\operatorname{Tan} \theta_{1}} Distance by which Lil moves closer to the building = x = 9.14 x 102 ft = 914 ft New distance of Lil from the building = d2 New angle of elevation of the spire atop the building = theta2 = 26.9o From the figure, \operatorname{Tan} \theta_{2}=\frac{h}{d_{2}} d_{2}=\frac{h}{\operatorname{Tan} \theta_{2}} From the figure, d_{1}=x+d_{2} \frac{h}{\operatorname{Tan} \theta_{1}}=x+\frac{h}{\operatorname{Tan} \theta_{2}} h\left(\frac{1}{\operatorname{Tan} \theta_{1}}-\frac{1}{\operatorname{Tan} \theta_{2}}\right)=x h=\frac{x}{\frac{1}{\operatorname{Tan} \theta_{1}}-\frac{1}{\operatorname{Tan} \theta_{2}}} h=\frac{914}{\frac{1}{\operatorname{Tan}(21)}-\frac{1}{\operatorname{Tan}(26.9)}} h = 1442 ft Height of the Empire State Building = 1442 ft ...