How do I find the altitude  of a trapezoid .?
605775
Are you talkin about a trapezium or a trapezoid.\nif its a trapezium,here's how : \nlet the height be "h".\ndrop two perpendiculars equal to h on the base.the lengths b&#92;w the perps.is 6 units.therefore the rest of the length is 10.each individual length to the left of the perp is 5 units.\nin the triangle with the diagonal,the side adjacent to the angle with the base and diagonal is 6+5=11\ntherefore the angle is cos^-1(11/12)=a\ntherefore tan a=h/11\ntherefore h=11tan a\nanswer is height,h=4.795831523
740147
If you have a TI-83 you can graph it and find it easily...\n\ny= button (plug in equation) ---> hit graph\n\nthen hit the second button(yellow)--->calc(same as trace button)\n\nbecause the graph was concave up you want to find a minimum...so click that...and simply enter once on the left side of the graph, once on the right, and then guess in the middle.  It will then give you the exact answer.\n\n(1,6) should be the correct coordinate.
554282
A = base * height\n\nbase = 8\n\nslant height = 6\nto get the actuall height, we use trig\n\nthink of 6 as the hypotenuse\n\nsin 30 = height / slant height\n\nor height = sin30 * 6\n\nheight = 3\n\ntherefore area = 8 * 3 = 24
494278
a trapezoid.\n   __\n  /__&#92;
797921
"A trapezoid is a 4-sided figure with one pair of parallel sides. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2." The height is the perpendicular distance between the two parallel bases.\n\nArea (trapezoid) = 1/2 h (b1 + b2) , where b1 and b2 are the lengths of the two parallel sides, and h is the perpendicular distance between them.
15842
Check the definition of a trapezoid.
1076556
Altitude\n(feet)   Adjustment\n(inches)      Altitude\n(feet)   Adjustment\n(inches)  \n\n50  \nAdd 0.06      \n550  \nAdd 0.59   \n\n100  \nAdd 0.12     \n600  \nAdd 0.64   \n\n150  \nAdd 0.17     \n650  \nAdd 0.69   \n\n200  \nAdd 0.22     \n700  \nAdd 0.74   \n\n250  \nAdd 0.27     \n750  \nAdd 0.79   \n\n300  \nAdd 0.33     \n800  \nAdd 0.84   \n\n350  \nAdd 0.38     \n850  \nAdd 0.89   \n\n400  \nAdd 0.43     \n900  \nAdd 0.94   \n\n450  \nAdd 0.48     \n950  \nAdd 0.99   \n\n500  \nAdd 0.54     \n1000  \nAdd 1.04
703199
It is an exercise in elementary calculus to show that (ignoring air resistance) the elevation angle for maximum distance is 45 degrees.  The vertical velocity of the egg will be zero at the peak height, and will increase as v = gt^2/2 until it hits the ground.  Energy is conserved, so the vertical velocity when it strikes the ground will match the vertical velocity with which it was launched, and the horizontal velocity will be constant.   This is enough data to solve the whole thing, but there is a shortcut: in the parabolic path at issue, it is always true that the peak height is 1/4 of the horizontal distance.  Hence, the peak height here is 24.225 meters, and that makes it trivial to compute the time and hence the velocity.
872821
You can prove it geometrically:\nhttp://www.mathwords.com/m/median_of_a_trapezoid.htm
309749
Altitude -0.8° 58.2° -0.8°
728290
The method is entirely dependent on what you know about the triangle in the first place.  If you know the 3 sides, you can use Steve's law for the altitude; ex: (alt to side c) = sqrt(4a^2b^2-(a^2+b^2-c^2)^2) / 2c\n\nIn general, the altitudes of a triangle intersect at a point called the orthocenter, whose location is described in detail at\nhttp://www.cut-the-knot.org/triangle/altitudes.shtml
772033
Draw a picture of it with arrows representing the vertical and horizontal velocities as 2 legs of a right triangle.  This triangle will show you that the angle with the vertical is arctan 3.5/5.5 = theta\n\nThen the flight path V will be Vv/cos(theta) or Vh/sin(theta)\n\nSince you're ruling out pythagoras, you really need to find the angle first, then the speed.......
74923
actually its not\n the answer would be (sin(30degrees)*200)+5\nsin(30degrees) is .5\n.5*200 = 100 +5 = 105 feet in elevation\n\ndraw a picture and label everything as much as possible, you eralize that you have the length of a hypotenuse, so you take teh sin of the angle then multiply by the length of the hypotenuse to get the length of the opposite side, that gives you teh height from eye level, you now must add the level you are looking from (5ft)\n\nhope this helps!!
332070
Partition this into parts of known sizes ,then calculate weights  of each part and its cent of gravity. Then take a point outside the assy. The moment of each part about this point equals the total weight times  the dist of the CG from this point. Repeat this process to find the vert and horiz position of the CG.Consider a letter L shape.,height l1,cross secton a1,b1 inches.weight=w1=l1*a1*b1*0.284 (steel) lbs.Bottom of L  , length l2, cross sectio a2,b2. weight=w2=l2*a2*b2*0.284 lbs.Then dist of CG from corner of L is w2*l2/(2*(w1+w2)), and dist up from corner is \nw1*l1/(2*(w1+w2)).- I hope ?
1031813
use the formula pi*r^2*h\nwhere pi=1.34\n r=radius (in inches)\n  h=height of cylinder (inches)
188413
Draw a picture.  You have 2 right triangles, with the satellite in the middle perpindicular to the ground.  Call this height "x"\n\nThen you have a right triangle coming off this height going off to the left with a lower-left angle of 37 degrees.  Another right triangle to the right with a lower-right angle of 57 degrees.  This will make one big triangle, with the height of the satellite coming down from the top vertex to somewhere along the bottom side.\n\nYou know that the entire length of this bottom side is 54, but you don't know how to divide it up.  Call the distance from the first observer (on the left) to the tower "y", and then the remaining distance will be "54-y"\n\nNow you have 2 variables, and enough information to create 2 equations:\n\ntan(31)= x/(54-y)\ntan(37)=x/y\n\nBy multiplying both sides of the second equation by "y" you get y*tan(37)=x; now you can substitute y*tan(37) back into the first equation\n\ntan(31)=(y*tan(37))/(54-y)  now it's just simple algebra.  But be careful, once you've solved it you have solved for y, so be sure to go back and find x.
411926
The height of a triangle is defined as the perpendicular distance from an angle to a side.  Now, since this is a right triangle, and depending on how it is situated, the height could be 10" or 12" if you observe from the two acute angles.  But from the right angle, the height goes from the angle to AC (your hypotenuse).  Finding this one will be tricky but can be done using the Pythagorean Theorem.\n\nIf you drop a height from the right angle to the hypotenuse, it breaks it into two parts.  The length of one part is x (since we don't know and since the height doesn't perfectly bisect the hypotenuse), and the length of the other part is 15.62-x (since the total length is 15.62").  It really doesn't matter which side is x, but for my explanation, I'll use x as the side closer to the leg that is 10".  This height creates two new right triangles, and you can use the Pythagorean Theorem to find out both the height and the missing side x.\n\nOne formula will end up being 10^2 = h^2 + x^2, and the other formula will end up being 12^2 = h^2 + (15.62-x)^2.  You can solve the first equation to find that h^2 = 100 - x^2 and substitute that in to the second equation:\n\n12^2 = h^2 + (15.62-x)^2\n144 = 100 - x^2 + 243.9844 - 31.24x + x^2\n144 = 343.9844 - 31.24x\n-199.9844 = -31.24x\nx = 6.4 (rounded)\n\nKnowing this, we can find that missing height:\nh^2 = 100 - x^2\nh^2 = 100 - (6.4)^2\nh^2 = 100 - 40.98\nh^2 = 59.02\nh = 7.68"\n\nSo it all depends on the specific height you're looking for - it's either 10", 12", or 7.68".\n\nAs for your trough, surface area is the sum of all the areas.  Break your trough into parts that you can find areas of.  If you're just looking for the outer surface area, for example, you have two triangles for the ends and two rectangles for the sides (assuming that it's an open trough).  The area of the triangles is A = 0.5bh, and the area of the rectangle sides is A = bh (b in this case will be a side of the trianlge, 2, and h will be the length of the trough, 16).  So just add up all the surfaces that will comprise your trough and you should have your surface area.  (I'm not sure if you need to include the inside as well, but if so you need 2 triangles and 2 rectangles for the outside, and 2 triangles and 2 rectangles for the inside as well.)