a sailor sits a 13.4 angle of elevation to the lighthouse. a chart lists the light as 239 ft. above sea level with a shallow reef at a 655 ft. radius from the base of the light house how far is the boat from the reef
+33616 If d is the distance of the boat from the lighthouse then
tan(13.4°) = 239/d or d = 239/tan(13.4°) so the boat is d - 655 ft from the shallow reef:
$${\frac{{\mathtt{239}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{13.4}}^\circ\right)}}}{\mathtt{\,-\,}}{\mathtt{655}} = {\mathtt{348.216\: \!993\: \!063\: \!345\: \!862\: \!1}}$$
The boat is approximately 348 ft from the reef.
+33616 If d is the distance of the boat from the lighthouse then
tan(13.4°) = 239/d or d = 239/tan(13.4°) so the boat is d - 655 ft from the shallow reef:
$${\frac{{\mathtt{239}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{13.4}}^\circ\right)}}}{\mathtt{\,-\,}}{\mathtt{655}} = {\mathtt{348.216\: \!993\: \!063\: \!345\: \!862\: \!1}}$$
The boat is approximately 348 ft from the reef.
