A billboard is positioned at the top of a 200ft tall building. From a point on the ground is the same level as the base of the building, the angle of elevation of the top and the bottom of the billboard is 75.3D and 61.4D, respectively. How tall is the building (with the billboard?)

Question

anonymous · Answer

Let x be the height of the billboard and the building together.$$\frac{x}{(200\text{Cot}[61.4{}^{\circ}])}=\text{Tan}[75.3{}^{\circ}]$$|dw:1317918101043:dw|

anonymous · Answer

$$x=\text{Tan}[75.3{}^{\circ}](200\text{Cot}[61.4{}^{\circ}])=415.6 \text{ft} $$