Question 1182191: A tripod is made of three sticks, each 5 ft. long, by tying together the ends of the sticks, the other
ends resting on the ground 3 ft. apart. Find the height of the tripod.
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
I will tell you HOW to find the answer, and then I'll give you the answer.
Then, if you are using this forum the way it is supposed to be used, you will go through the steps and see if you get that answer.
View the tripod and the ground as a pyramid with an equilateral triangle as a base. Each edge of the base is 3; each other edge of the pyramid is 5.
(1) Find the slant height of each face of the pyramid.
Pick one of the three faces of the pyramid and draw the perpendicular to the base, bisecting the base. That will give you a right triangle with hypotenuse 5 and one leg (1/2)3 = 3/2 or 1.5. The other leg of this right triangle is the slant height of each face. Find that length using the Pythagorean Theorem.
(2) The height of the pyramid is the distance from the center of the base to the peak. Picture the three altitudes of the triangular base intersecting at the center of the base.
(3) Look a the right triangle with the height as one leg, the distance from the center of one edge of the base to the center of the base, and the slant height from step (1) as the hypotenuse. Determine the height again using the Pythagorean Theorem.
To do step (3), you need to know the distance from the center of an edge of the base to the center of the base. I will tell you that much -- it is sqrt(3)/2 inches. If you have the desire to derive that fact on your own, draw an equilateral triangle with its three altitudes and observe that the distance from the center of one side of the triangle to the center of the triangle is the short leg of a 30-60-90 right triangle with a long leg equal to half the length of the side of the equilateral triangle.
Using 3 as the side length of the equilateral triangle should give you the sqrt(3)/2 answer.
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ANSWER: The height of the tripod (pyramid) is sqrt(22) inches.
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