a gorge with a rectangular cross section is 60m wide. The angle of depression of a bottom corner, when viewed from the opposite edge is 72 degrees
a)How deep is the gorge
b)if the angle of depression were 80 degrees, would the gorge be deeper or shallower.
2006-08-02 08:45:30 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
If I understand your question correctly.
Angle of 72° => 18° incline (90° - 72°).
(1)
Opp. = 60 tan 18°
Opp. = (60)(0∙324919696)
Opp. = 19∙49518177 Meters.
(2)
Opp. = (60)(tan 10°)
Opp. = 10∙57961884 Meters.
This implies the gorge will be shallower.
2006-08-02 08:57:38 · answer #1 · answered by Brenmore 5 · 0⤊ 0⤋
I second flori's answer.
It also helps to know the difference between a canyon and a gorge. A gorge is deeper than it is wide, while a canyon is wider than it is deep. So you know your answer has to be greater than 60 meters.
2006-08-02 17:43:29 · answer #2 · answered by Bob G 6 · 0⤊ 0⤋
angle of depression= angle of elevation(alternate interior angles are equal)
depth= 60tan72
= 60x 3.078
= 184.68 meter
when angle of depreesion is 80 degree then depth=60tan80
= 60x5.67
=340.2
so when angle is 80 degree then gorge will be deeper.
note:- this type of questions need good diagram with help of pen tablet.
2006-08-02 16:20:15 · answer #3 · answered by flori 4 · 0⤊ 0⤋