How do i find the right triangles base and height when there are alot of digits

Suppose you have a triangle with sides {6,7,8} — how do you find the height?This is a question some GMAT test takers ask.  They know they would need the height to find the area, so they worry: how would I find that height.  The short answer is:fuhgeddaboudit! Which height?First of all, the “height” of a triangle is its altitude.  Any triangle has three altitudes, and therefore has three heights.  You see, any side can be a base.  From any one vertex, you can draw a line that is perpendicular to the opposite base — that’s the altitude to this base.  Any triangle has three altitudes and three bases.  You can use any one altitude-base pair to find the area of the triangle, via the formula A = (1/2)bh.
In each of those diagrams, the triangle ABC is the same. The green line is the altitude, the “height”, and the side with the red perpendicular square on it is the “base.”  All three sides of the triangle get a turn. Finding a heightGiven the lengths of three sides of a triangle, the only way one would be able to find a height and the area from the sides alone would involve trigonometry, which is well beyond the scope of the GMAT.  You are 100% NOT responsible for knowing how to perform these calculations.  This is several levels of advanced stuff beyond the math you need to know.  Don’t worry about that stuff.In practice, if the GMAT problem wants you to calculate the area of a triangle, they would have to give you the height.  The only exception would be a right triangle — in a right triangle, if one of the legs is the base, the other leg is the altitude, the height, so it’s particularly easy to find the area of right triangles. Some “more than you need to know” caveatsIf you don’t want to know anything about this topic that you don’t absolutely need for the GMAT, skip this section!a. Technically, if you know the three sides of a triangle, you could find the area from something called Heron’s formula, but that’s also more than the GMAT will expect you to know.   More than you needed to know!b. If one of the angles of the triangle is obtuse, then the altitudes to either base adjacent to this obtuse angle are outside of the triangle.  Super-technically, an altitude is not a segment through a vertex perpendicular to the opposite base, but instead, a segment through a vertex perpendicular to the line containing the opposite base.In the diagram above, in triangle DEF, one of the three altitudes is DG, which goes from vertex D to the infinite straight line that contains side EF.  That’s a technicality the GMAT will not test or expect you to know.  Again, more than you needed to know!c. If the three sides of a triangle are all nice pretty positive integers, then in all likelihood, the actual mathematical value of the altitudes will be ugly decimals.  Many GMAT prep sources and teachers in general will gloss over that, and for the purposes of easy problem-solving, give you a nice pretty positive integer for the altitude also.  For example, the real value of the altitude from C to AB in the 6-7-8 triangle at the top is:Not only are you 100% NOT expected to know how to find that number, but also most GMAT practice question writers will spare you the ugly details and just tell you, for example, altitude = 5.  That makes it very easy to calculate the area.  Yes, technically, it’s a white lie, but one that spares the poor students a bunch of ugly decimal math with which they needn’t concern themselves.  Actually, math teachers of all levels do this all the time — little white mathematical lies, to spare students details they don’t need to know.So far as I can tell, the folks who write the GMAT itself are sticklers for truth of all kinds, and do not even do this “simplify things for the student” kind of white lying.  They are more likely to circumvent the entire issue, for example, by making all the relevant lengths variables or something like that.   Yet again, more than you needed to know! What you need to knowYou need to know basic geometry.  Yes, there is tons of math beyond this, and tons more you could know about triangles and their properties, but you are not responsible for any of that.  You just need to know the basic geometry of triangles, including the formula A = (1/2)b*h.  If the triangle is not a right triangle, you have absolute no responsibility for knowing how to find the height — it will always be given if you need it.   Here’s a free practice question for you.

You should automatically already have the height to answer the question your being asked even if there are a lot of digits

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle