How to find length of a Non Right Triangle, given just one side and one angle?
Any non right triangle, like, Isosoles, Scalene? And you’re given one side, and one angle, you have to find the other sides? Formulas?
depends on the side and angle given
say you have an isosceles triangle
it gives you the side on the left, so it’s lets say, 6
(which means two sides are 6, the ‘left and right’)
and the angle given is at the bottom left, and say it’s 30 degrees. (also, the bottom RIGHT is 30 degrees because in isosc. triangles base angles are congruent)
draw an altitude from the top angle (in between the two sides with lengthts of 6) to the base, in the middle of it.
this creates a right angle on the base
so you are left with half a triangle on each side, with the left length of 6, the left angle of 30, the right angle of 90, and the top angle of 60. (each triangles’ angles add up to 180)
now you can do the 30-60-90 theorem
opp 30 = x
opp 60 = x radical 3
opp 90 = 2x
so the length of 6 is opposite the 90 degree angle.
therefore, 6 = 2x, because (2x = opposite 90)
x = 3
so opposite the 30 degree angle, (the altitude) is 3 units
opposite the 60 is x radical 3, or 3 radical 3
HALF OF THE BASE IS 3 RADICAL 3 (because the altitude bisected the base, and the angles)
the base is 3 radical 3 plus 3 radical 3, which = 6 radical 3
you have sides of 12 (the two equal sides which are 6) and the base, which is 6 radical 3
so the length of the triangle is
12 + 6 radical 3 units (6 radical 3 is 6 times the square root of 3)
DJmag MicroMix (old one, non participating)
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