Dream4Life

i cant seem to figure out number 19 on page 401 of the BB. can some one give me an explantion of how to solve it.

rspence

Do you mind posting the question? I don't have the blue book.

Dream4Life

well actaully it was a figure, a triangular prism. one of the edges ( of the faace of a triangle) was referred to as "e". the bottom of the figure was a rectangle ( or sqaure i think), with one of the edges referred to as "m". they wanted you to find the height of the triangular prism in terms of m, and also said that "e = m". i know this has to do with just splitting up the figures into special right tri. ( 30,60,90), but i cant find my answer and the answer that they said was m/rad 2.

rspence

Sorry, I can't understand your last post. Which edges are labeled e,m? Can you post the entire question, as-is? Thanks

Dream4Life

ok, picture this. a triangular prisim with a square base. maybe you should draaw it out. so its basically four isosceles triangles connected at the bottom by the four edegs of a quare. the edge where the sides of two of the icoc. tri. meet is e. the edge of the side of a sqaure is m. e an m are equal( yeah, i dont know how this is possible). they want u to find the height of the figure, from the base to the tip where all four faces meet, in terms of m. this is basically whats in the book, except much less wordy becasue they have a fiugre to show it.

rspence

That's a pyramid, not a prism.

Other than that, I've solved it. Basically, all the edges of the pyramid are equal, and e=m implies that the triangles are all equilateral.

Let A be the apex of the pyramid, and B be the center of the square base (so that AB is the height). Let C be any of the other four vertices. Clearly, AC = m. Also, BC = (m sqrt(2))/2 because 2BC is the diagonal of a square with side length m.

ABC is a right triangle with hypotenuse m and side length (m sqrt(2))/2. To find AB, we use Pythagorean theorem, or note that AC = BC sqrt(2). In either case, ABC is a 45-45-90 triangle, so AB = BC = (m sqrt(2))/2. AB is the height of the pyramid, so we're done.

Dream4Life

i get what you are saying, but the answer key says that the ans. is m/ rad 2, care to explain=)

rspence

Umm...m/(sqrt(2)) is the same as (m sqrt(2))/2...