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the angles of elevation to the bird's nest are 30 degrees and 60 deg. How far is each observer from the base of the tree?
We don't just want the answer, but would like to know a step by step on how to do it also. THANK YOU!!! (We won't forget to pick the best answer)

2007-01-28 09:04:22 · 4 answers · asked by TJTB 7 in Science & Mathematics Mathematics

I'm going to have a hard time picking best answer, but I just want to thank each of you for contributing. We actually got a little from most answers to clearify. THANKS TO EACH OF YOU!!! ;o)

2007-01-28 11:57:52 · update #1

Northstar was the only person who put the two observers on the same side of the tree, like we had done. We thought we were getting the wrong answer, but she proved that you were all right and so were we and it depended on where we placed those two crazy observers!!!!

2007-01-28 12:00:35 · update #2

4 answers

I assume the two observers are on the same side of the tree.

Let
h = height of tree
x = distance of closest observer to tree
x + 200 = distance of second observer

Then we have two right triangles. For both the opposite leg is h. For the first observer the adjacent leg is x. For the second observer it is x + 200. So we have

tan 30° = h/(x + 200) = 1/√3
tan 60° = h/x = √3

h = (x + 200)/√3 = x√3
x + 200 = 3x
200 = 2x
x = 100
x + 200 = 300

So the two observers are 100 and 300 feet from the tree.

By similar reasoning, if the two observers were on opposite sides of the tree they would be 50 and 150 feet from the tree.

2007-01-28 10:08:47 · answer #1 · answered by Northstar 7 · 1 0

First draw a diagram, kind of tricky on yahoo.
It needs to look like a tent with a stick in the middle. the two angles are on the outside and the stick is the tree.
You need to find the side thats next to the angle (adjacent) on each triangle (the one that represents the ground), and the thing the triangles have in common is the side opposite the angle, so we use tangent rule
tanθ = opp/adj
we know the opposite sides to the angles on both triangles are the same so if a and b are the distances between each observer and the tree (the adj of each triangle)
a x tan30 = opp = b x tan60

tan30 = 1/√3 and tan60 = √3

so a/√3 = b√3
multiply by √3
a = 3b

and we know a + b = 200 feet
so a = 50 feet, b = 150 feet
Also, we can find the height of the bird's nest (call it x)
tan30 = x/b
150/√3 = x
x = 86.6 feet

2007-01-28 09:40:36 · answer #2 · answered by Lydia 2 · 0 0

This is a right triangle type problem. That is, 30, 60, 90 degrees=180 degrees in one triangle.

Solve it like you would using the Pythagorean Theorem.

The 200' could be used as the hypotenuse [ "c" ] . Distances from the nest to person "A" could be the "a" side and from the nest to person "B" the "b" side.

The 90degree angle would be @ the bird's nest. The 30 degree angle would be @ either person on the ground with the 60 degree angle @ the other person on the ground.

a2 + b2 = c2

2007-01-28 09:17:27 · answer #3 · answered by James R 5 · 0 0

►not much trig really. observer A is at x feet from the tree. Observer B is at (200-x) feet from the tree, the height of the nest being h;
for observer A h=tan(60)*x; for observer B h=tan(30)*(200-x); hence tan(60)*x = tan(30)*(200-x) or x*sqrt3 =200*(1/sqrt3) –x*(1/sqrt3); thus 3x=200-x and x=50ft
200-50 =150ft;

2007-01-28 11:21:52 · answer #4 · answered by Anonymous · 0 0

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