at a particular time, a tree casts a shadow 28m long on the ground. at the same time, a nearby vertical pole that is 3 feet tall casts a shadow 4 feet long. how tall is the tree
2006-10-27 07:40:49 · 9 answers · asked by mandi_albie14 1 in Science & Mathematics ➔ Mathematics
At a given moment, the ratio of an object's height to the length of its shadow is constant. That means that if h is the height of the tree, y/28 = 3/4 ==> y = 0.75*28 = 21 m.
2006-10-27 07:43:20 · answer #1 · answered by DavidK93 7 · 0⤊ 1⤋
The only way you can solve for this is to assume that the ground under the two shadows has a constant slope so that the length of the pole's shadow in proportion to the poles height is the same as the tree's shadow in proportion to the trees height. poles height = 3/4*pole's shadow so tree's height = 3/4 * tree's shadow. I know it's a bit artificial and if the ground suddenly dips or rises beyond the tip of the pole's shadow, the answer will be completely wrong, but there you go. This is math.
2006-10-27 08:00:01 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Setup a proportion let me show you
x/28 = 3/4
Now cross multiply
4x = 84
Solve for x (Divide both sides by 4)
x = 21
2006-10-27 07:44:45 · answer #3 · answered by Up_In_Smoke 2 · 0⤊ 0⤋
21
tan@ = 3/4
tan@ = length of tree / 28
3/4 = legnth of tree / 28
length of tree = 28*3/4 = 21
2006-10-27 07:59:21 · answer #4 · answered by Kala Rajesh R 1 · 0⤊ 0⤋
It's a ratio question: 3:4 as x:28
Solve for x. Cross-multiplying is probably what you learned in class.
2006-10-27 07:45:58 · answer #5 · answered by Anonymous · 0⤊ 0⤋
21 meters
2006-10-27 07:49:57 · answer #6 · answered by jemko17 1 · 0⤊ 0⤋
21 metres
2006-10-27 07:45:03 · answer #7 · answered by Anonymous · 0⤊ 0⤋
..|\......................|\
x|...\...................|...\
..|.....\..........3 ft.|.....\
..|__A(\..............|__Q(\
...28m...............4 feet
Tree-------------------Pole
Hope you understand the figure
Since it is the same time, angle made by both the tree and the pole will be the same=> tanQ=tanA=>3/4=x/28(tanQ=Perpendicular /base) => x=(3X28)/4
=21 m...
2006-10-27 07:57:13 · answer #8 · answered by Chirag Jain 1 · 0⤊ 0⤋
21m.
2006-10-27 07:44:40 · answer #9 · answered by Crystaly s 1 · 0⤊ 0⤋