Two pilots take off from the same airport. Mason heads due south. Nancy heads 23º west of south. After 400 land miles, how far is Nancy from Mason’s route? Round your answer to the nearest tenth of a mile. (Enter only the number.)
+33616 Assuming they both travel at the same speed and, hence both have travelled 400 miles, then the paths they have taken, together with the straight line between their end points, form an isosceles triangle. If the distance between them is x then
x/2 = 400*sin(23°/2) so x = 800*sin(11.5°) miles
$${\mathtt{x}} = {\mathtt{800}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{11.5}}^\circ\right)} \Rightarrow {\mathtt{x}} = {\mathtt{159.494\: \!347\: \!533\: \!6}}$$
x = 159.5 miles to the nearest tenth of a mile.
+23248 How fast are they going?
I don't understand "After 400 land miles"; is that for one of them, for both of them?
+33616 Assuming they both travel at the same speed and, hence both have travelled 400 miles, then the paths they have taken, together with the straight line between their end points, form an isosceles triangle. If the distance between them is x then
x/2 = 400*sin(23°/2) so x = 800*sin(11.5°) miles
$${\mathtt{x}} = {\mathtt{800}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{11.5}}^\circ\right)} \Rightarrow {\mathtt{x}} = {\mathtt{159.494\: \!347\: \!533\: \!6}}$$
x = 159.5 miles to the nearest tenth of a mile.
