in triangle CBS the measure of angle c is 70 degrees. which of the following measures for triangle CBS will create exactly one triangle?
1. measure of angle B=30 degrees and measure of angle S=80 degrees
2. line CB=16 and measure of angle B = 50 degrees
3. line CB=20 and line SB=15
Answers:
A.) #1 only
B.)#2 only
C.)#1 and #2 only
D.)#2 and #3 only
2007-01-07 09:32:35 · 6 answers · asked by hi 3 in Science & Mathematics ➔ Mathematics
a friend said that it was C
2007-01-07 09:39:38 · update #1
1) the triangles are similar but not necessarilly congruent (AAA)
2) Triangles are congruent by ASA
3) from the law of cosines
15^2=20^2+x^2-2*20x cos 70
225=400+x^2-40x cos 70
x^2-13.68x+175
x=(13.68+/-√(13.68^2-4*175))/2
x=6.84+/-.5√(187.1424-700)
x=6.84+/-√-512.86
no such triangle is possible
This can also be proved from the law of signs.
sin s/20=sin 70/15
sin s=4/ sin 70=1.25
s=arcsin 1.25 which doesn't exist.
Therefore the answer is B) #2 only
2007-01-07 10:07:42 · answer #1 · answered by yupchagee 7 · 15⤊ 0⤋
The answer is B and here is why:
1 is AAA and that creates infinitely many triangles, just enlarged
3 is SSA which could give either 0, 1, or 2 triangles; in this case it gives no triangles (the 15 side is too short to reach the other side
but 2 is ASA which goves only one triangle
2007-01-07 09:39:39 · answer #2 · answered by hayharbr 7 · 0⤊ 0⤋
are you seriously asking this?? You need to study more! but, the answer is A
2007-01-07 09:36:06 · answer #3 · answered by jpferrierjr 4 · 0⤊ 2⤋
answer A
2007-01-07 09:37:17 · answer #4 · answered by Anirudh T 3 · 0⤊ 1⤋
answer is C, I suppose
2007-01-07 10:22:17 · answer #5 · answered by James Chan 4 · 0⤊ 0⤋
it has got to be A and cool u what???
2007-01-07 09:52:23 · answer #6 · answered by Smarcher7623 2 · 0⤊ 1⤋