From the top of a building 60 feet high, the angle of elevation of the top of a pole is 14 degrees. At the bottom of the building the angle of elevation of the top of the pole is 28 degrees. Find the distance from the pole to the building.
+33661 Let h be the height of the pole and d be the distance from the building.
tan(28) = h/d ...(1)
tan(14) = (h-60)/d ...(2)
Rewrite (2) as tan(14) = h/d - 60/d ...(3)
Use (1) in (3): tan(14) = tan(28) - 60/d ...(4)
Rearrange (4) to get d = 60/(tan(28)-tan(14))
$${\mathtt{d}} = {\frac{{\mathtt{60}}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{28}}^\circ\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{14}}^\circ\right)}\right)}} \Rightarrow {\mathtt{d}} = {\mathtt{212.478\: \!562\: \!245\: \!221\: \!509\: \!7}}$$
or d ≈ 212.5 ft
+33661 Let h be the height of the pole and d be the distance from the building.
tan(28) = h/d ...(1)
tan(14) = (h-60)/d ...(2)
Rewrite (2) as tan(14) = h/d - 60/d ...(3)
Use (1) in (3): tan(14) = tan(28) - 60/d ...(4)
Rearrange (4) to get d = 60/(tan(28)-tan(14))
$${\mathtt{d}} = {\frac{{\mathtt{60}}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{28}}^\circ\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{14}}^\circ\right)}\right)}} \Rightarrow {\mathtt{d}} = {\mathtt{212.478\: \!562\: \!245\: \!221\: \!509\: \!7}}$$
or d ≈ 212.5 ft
