2007-04-10 03:13:09 · 5 answers · asked by elson7997 1 in Science & Mathematics ➔ Mathematics
labeling the tringle
a triangle has a vertex A or Angle A.
Opposite angle A is little " a " which represents the opposite side, or y axis. therefore a = y
Sinθ = y / r
sin40 = 5 / r
r sin 40 = r(5/r)
rsin40 = 5
rsin40 / sin40 = 5 / sin40
r = 5 / sin40
r = 5 / 0.64278761
r = 7.778619134
r = 7.8 rounded up to one decimal place
sparknotes.com/math/trigonometry/solvingrighttriangles/section1.html
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2007-04-10 04:50:17 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
By virtue that you have the angle and its opposite side,
you can use the sine's law:
a / sinA = b / sinB = c / sinC
since C = 90,
sinC = sin90 = 1
Therefore,
c = a / sinA = b / sinB
So what do we know?
we know that
A = 40 degrees,
B = 90 - 40 = 50 degrees.
C = 90 degrees.
Therefore, A + B + C = 180 degrees
So by using the sine's law:
sinA/a = sinB/b
sin50 = 0.766044443118978
sin40 = 0.642787609686539
b = a * (sinB / sinA) = 5 * sin50 / sin40
= 5 * 1.19175359259421
= 5.95876796297105
Therefore,
b = 5.95876796297105
REMEMBER THAT the angles are proportions
and side are the measures.
It is ever needed to specify well the dimensions
of the triangle, otherwise it will likely have infinite
solutions.
2007-04-10 10:56:00 · answer #2 · answered by theWiseTechie 3 · 0⤊ 0⤋
I agree with Daniel. Specify which angle and which side. Are them opposite or adjacent?
Ana
2007-04-10 10:25:40 · answer #3 · answered by MathTutor 6 · 0⤊ 0⤋
tan(40) = B/5
B = tan(40) * 5 = 4.1954981558864000588156364906159
2007-04-10 10:18:15 · answer #4 · answered by Dave 6 · 0⤊ 0⤋
Which angle is the right angle?
2007-04-10 10:16:20 · answer #5 · answered by Daniel 3 · 0⤊ 0⤋