a 90 ft tree casts a shadow that is 140 ft long. What is the angle of elevation of the sun?
+33665 Here you have a right-angled triangle with the opposite side = 90ft and the adjacent side = 140ft, so you need to use the inverse tangent function (as tan(A) = opposite/adjacent)
$${\mathtt{A}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{90}}}{{\mathtt{140}}}}\right)} \Rightarrow {\mathtt{A}} = {\mathtt{32.735\: \!226\: \!272\: \!108^{\circ}}}$$
Angle of elevation ≈ 32.7°
+33665 Here you have a right-angled triangle with the opposite side = 90ft and the adjacent side = 140ft, so you need to use the inverse tangent function (as tan(A) = opposite/adjacent)
$${\mathtt{A}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{90}}}{{\mathtt{140}}}}\right)} \Rightarrow {\mathtt{A}} = {\mathtt{32.735\: \!226\: \!272\: \!108^{\circ}}}$$
Angle of elevation ≈ 32.7°
