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If sin(x) = four fifths, then cos(x) = three fifths.
Sin-1(0.8) = 53.13 degrees.
Cos(53.13) = 0.6.
There are many ways you could work this out. One of them is to use the relationship between the squares of the sine and cosine:
sin2(x) = 1 - cos2(x)
(4/5)2 = 1 - cos2(x)
16/25 = 1 - cos2(x)
-cos2(x) = - 1 + 16/25
cos2(x) = 1 - 16/25
cos2(x) = 9/25
cos(x) = ±3/5
You could also work it out using good ol' Pythagorean theorem:
Let:
a ≡ adjacent
o ≡ opposite
h ≡ hypotenuse
Then we know:
sine = o/h
cosine = a/h
h2 = a2 + o2
We already have our opposite and hypotenuse sides, as we're given those with the value of the sine. We need to work out the adjacent side then:
h2 = a2 + o2
∴ a2 = h2 - o2
∴ a = (h2 - o2)1/2
∴ a = (52 - 42)1/2
∴ a = (25 - 16)1/2
∴ a = 91/2
∴ a = ±3
And now that we have the length of the adjacent side, as well as the hypotenuse, we know the cosine of the angle as that is is the ratio between the two:
cosine = a/h
∴cosine = ±3/5
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How do i find length of AB in the triangleABC angleB equals 95 degrees angleC equals 24 degrees and line AC equals 17cm how do i find the length of AB?
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In a triangle ABC b equals 15 cm and c equals 25 cm and also angle B equals 32'15'Find the side a and other angles?
By the sine rule, sin(C)/c = sin(B)/b so sin(C) = 25/15*sin(32d15m) = 0.8894 so C = 62.8 deg or 117.2 deg. Therefore, A = 180 - (B+C) = 85.0 deg or 30.5 deg and then, using the sine rule again, a/sin(A) = b/sin(B) so a = sin(A)*b/sin(B) = 28 or a = 14.3
