trigonometry problem?

Question

To estimate the height of a tree,two people position themselves 25 feet aprt. From the first person, the bearing of the tree is N 48 degree E and the angle of elevation to the top of the tree is 73 degree. if the bearing of the tree from the second person is N 38 degree W, estimate the height of the tree to the nearest foot.
PLEASE SHOW ME THE FIGURE, I DON'T KNOW HOT TO DRAW IT, THAT'S MY QUESTION.

I saw the diagram, that makes sense, and I got the right answer. But one thing I can't understand, how can u unfold that? I got the answer from the second diagram. And how u the tree line is vertical line?

Answer 1

Here is a diagram:

http://math.colgate.edu/~kellen/interspace/treelo.gif

For a higher resolution version (not recommended for dial-up users), click here:

http://math.colgate.edu/~kellen/interspace/treehi.gif

I may find the time to solve this too, and edit my answer with the solution, but you said you wanted to know how to draw it, so here it is. If I get more of a solution to help you, I will post it.

PS I find it hilarious that someone is suggesting you draw points in a 3-dimensional space. Since when is paper 3-dimensional?

Answer 2

I suppose you'd have to draw a three dimensional figure for this one. To draw it, first draw a triangle with two points at the bottom, A and B, and one at the top, T. Now draw a vertical line from the top point, T, partway down towards the base of the triangle... this is the tree. From the bottom of that line, a point we'll call G for ground, draw two lines - each should go from the bottom of the vertical line (point G) to one of the remaining points (A and B... so make two new line segments GA and GB). Now you should have something that looks like the citgo logo:

http://www.citgo.com/Images/CITGOColorLogoNoLine.gif

The top point T of the triangle is the top of the tree. G is the base of the tree. The lower left point A is the first person and the lower right point B is the second person. The line segment AB is 25 feet long. The tricky part is drawing the angles. The angle of elevation (73 deg) is drawn between the lines AT and AG. If N 48degree E means a 48 degree angle towards "east" (though I'm not sure if I'm interpreting that right... are the people facing north? I'm assuming so...) , then the angle between AG and AB is 90 - 48 = 42 and the angle between BG and BA is 90 - 38 = 52.

Hope that helps... sorry I didn't draw it though

Answer 3

You need to draw a 3-dimensional coordinate system. the x and y axes are perpendicular to each other and the z -axis is perpendicular to both of them at their point of intersection. Sort of like the where 3 edges of a cube meet. The origin is (0.0.0) or the corner of the cube mening x=y=z=0.

Let person 1 be at (0,0,0) and person 2 be at (25,0,0). Let the positive y-axis be North. Draw a line from the origin that makes a 48 degree angle with the y -axis and is to the right (East) of the y-axis. Now draw a line from (25,0,0) that makes a 38 degree angle with a line parallel to the y-axis and to the left (West) of this line. The intersction of these two lines in the xy plane is the location of the tree. Its coordinates is (25,y,0)

Now erect a perpendicular at this point parallel to the z-axis. Make the height of ths line z units so it is at the point(25,y,z)

Now draw a line from the origin to the (25, y,z) (the top of the tree)and another line to (25,y,0) (the foot of the tree). Make the angle between these two lines 73 degrees.

Your figure is now complete.

Answer 4

Inadequate information. Elevation from N 38 position not given. Can not be solved.