TO ESTIMATE THE HEIGHT OF A TREE,2 PEOPLE POSITON THEMSELVES 25FT APARt?

Question

TO ESTIMATE THE HEIGHT OF A TREE,2 PEOPLE POSITON THEMSELVES 25FT APART. FROM THE FIRST PERSON, THE BEARING OF THE TREE IS N48E AND THE ANGLE OF ELEVATION TO THE TOP OF THE TREE 73 DEGREES. IF THE BEARING OF THE TREE FROM THE SECOND PERSON I N38W, ESTIMATE THE HEIGHT OF THE TREE TO THE NEAREST FOOT.

Answer 1

I'm pretty sure you haven't provided quite enough information. Fenx above is right the 25-foot distance is east-west. The problem doesn't say that though.

If I understand "bearing", you mean that with respect to the first person, the tree is 48 degrees east of north, and with respect to the second person, it's 38 degrees west of north.

Assuming I got that right, then if the height of the tree is h, and the distance from the first person to the tree is d, then tan 73 = h/d, and h = d tan 73.

We need to get d.

For the second part of the problem, draw x-y axes and place the tree at point O, the origin. Draw a line from the "southwest" to the "northeast" passing through the origin and forming a 48 degree angle with the y-axis. Point A, the location of the first person, is somewhere on that line in the third quadrant.

Now draw another line running from "southeast" to "northwest", passing through the origin, and forming a 38 degree angle with the y-axis. The second person is located somewhere on that line in the fourth quadrant.

Since we haven't yet established any scale for this diagram, Points A and B can be placed on those lines in the third and fourth quadrants respectively. Either A or B can be closer to O, or they can be equidistant.

Once we've arbitrarily placed points A and B, draw a line connecting them, and indicate that AB has length 25. Also, we know that angle AOB = 48 + 38 = 86 degrees. We do know angles OAB or OBA, but their sum is 180 - 86 = 94 degrees. And the length d that we wanted from the first part of this problem is the side OA in this triangle.

The best we can do with the information we have is to use the Law of Sines: OA/sin OBA = AB/sin AOB = 25/sin 86.

Then, OA = 25(sin OBA/sin 86).

From that, you can get the height of the tree h:

h = 25 tan 73 (sin OBA/sin 86)

As I said up top, you need to provide more information. The best, I suppose, is the bearing of the second person relative to the first person. Another possibility is the angle of elevation of the treetop from the second person's location, although I'm not a hundred percent sure thatb would do the job.

By the way, the height of the tree is (25/sin 86) tan 73 =82 feet. That occurs when angle ABO is a right angle.

Answer 2

My answer is 64.60 feet. I arrived at this answer by setting up an equilateral triangle using the bearings that were given and the one distance of 25 feet. I computed the interior angles of the triangle by just subtracting the N48E bearing from 90 to arrive at an interior angle on the left side of the E-lateral Tri of 42 degrees. I used the same technique with the right side angle (N38W) and calculated an interior angle of 52 degrees. Then add these two angles and subtract from 180 to get the final angel of 86 degrees. Then use the law of Sines to get the side length of the triangle that includes the angle of elevation. Now simply solve the right triangle to arrive at the 64.60 feet. I hope this is correct.
Good luck.

Answer 3

It relies upon. Being on a bridge that's intense over the water bothers me, yet a bridge "nearer" to the water does no longer. Being on the precise of a tall construction, looking down bothers me... or maybe being on the backside of a tall construction and attempting to look instantly up, bothers me...yet... Being in an airplane does no longer. pass figgr!! each person is entitled to my opinion.

Answer 4

WHY?? who cares. what happened to the tape measure is really the most important question i believe. and if you really, really need to know the exact height. chop it down and measure it.

Answer 5

cut the tree down , then measure the length!!!!!