Can you answer these math questions?
If you can, also provide how you got the answer. I need to know these to continue to play NCAA CU football! :-O
- MathematicaLv 71 decade agoFavorite Answer
Since ABM is isosceles, that means AM = AB
also in BMN, then BM = BN
A median cuts the side into two equal halves.
AE = EB
AD = DM
and since AB = AM, then
AE = EB = AD = DM
Same for the other triangle
BP = PM = BC = CN
Also, in an isosceles triangle, the medians from the base angles are congruent. So...
BD = ME
NP = MC
So.... Using substitution:
AE + ME + MC + BC = 32
AE = AD
ME = BD
MC = NP
BC = BP
AD + BD + BP + NP = 32
ABN is equilateral, which means each of its angles is 60 degrees (and all three sides are equal length).
AM is a median, which means NM = MB.
Since NM = MB, AN = AB, and angle ANB = angle ABN = 60 degrees, then
triangle ANM is congruent to triangle ABM (by the side-angle-side theorem)
Because they are congruent, then corresponding parts of the triangles are congruent, which means
angle ANM = angle ABM
since angle NAB = 60 degrees (definition of equilateral triangle), and NAB = NAM + MAB
then NAB = MAB = 30 degrees.
Triangle AME is equilateral (given). So
angle AME = angle MEA = angle EAM = 60 degrees
since we know angle MAB = 30 degrees (from above),
and MAE = MAB + BAE
then BAE = 30 degrees.
Since we know AM = AE (equilateral triangle)
and AC = AC (reflexive property),
and angle MAC = angle CAE = 30
by side-angle-side, we again know that
triangle AMC is congruent to triangle AEC
Because corresponding parts of triangles are congruent, we know that MC = CE
Since MC = CE, then AC must be the median of triangle AME.
We know ABM is equilateral, that means all angles of that triangle are 60 degrees. So, angle AMB is 60 degrees.
Since BME are collinear (make a straight line), then you can find angle AMC.
AMC + AMB + CME = 180
AMC + 60 + 30 = 180
AMC = 90 degrees.
You can use trigonometry on triangle ACM (since it's a right triangle) to find AM.
sin (angle ACM) = (AM) / (AC)
sin 30 = AM / 36
1/2 = AM / 36
18 inches = AMSource(s): Sorry, I don't know how to do #4.