when ovserved from the top of a 250 ft tall lighthouse, the angle of depression of an approaching ship is 50 degrees. Identify the horizontal distance from the lighthouse to the ship rounded to the nearest foot
+33661 If A is the angle of depression, then tan(A) = height/distance, so distance = height/tan(A)
$${\mathtt{distance}} = {\frac{{\mathtt{250}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{50}}^\circ\right)}}} \Rightarrow {\mathtt{distance}} = {\mathtt{209.774\: \!907\: \!794\: \!356\: \!960\: \!3}}$$
distance = 210 ft to the nearest foot.
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+33661 If A is the angle of depression, then tan(A) = height/distance, so distance = height/tan(A)
$${\mathtt{distance}} = {\frac{{\mathtt{250}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{50}}^\circ\right)}}} \Rightarrow {\mathtt{distance}} = {\mathtt{209.774\: \!907\: \!794\: \!356\: \!960\: \!3}}$$
distance = 210 ft to the nearest foot.
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