Use sin, cos and tan in a right-angled triangle
Trigonemtry - Used when we know at least one side and one angle to find the other missing sides and angles
In a right-angled triangle:
the hypotenuse is the longest side (opposite the right angle)
the opposite and adjacent depend on the angle we are looking at 'x'
the opposite is the side opposite x
the adjacent is the side adjacent to x that is not the hypotenuse
We have 3 formula to relate these, we remember this by SOHCAHTOA (sock-ka-toe-ah)
SOH: Sin = Opposite/Hypotenuse
CAH: Cos = Adjacent/Hypotenuse
TOA: Tan = Opposite/Adjacent
Remember that Sin, Cos and Tan are linked with the angle (e.g Sin(x) where x is the angle)
We use each formula depending on what information we have.
Finding missing sides
We know angle A =
We know the hypotenuse side AC =
We want to find the opposite side BC.
We use SOH
SinA = AC/BC we can rearrange this to BC = AC/SinA
Finding missing angles
We know want to know angle D
We know the adjacent side DF =
We know the opposite EF =
We use TOA
TanD = EF/DF
We have to remember that 'Tan D' does not mean 'Tan multilplied by D', try it on your calculator! It doesn't work!
To get D on it's we must use inverse Tan (it's on your calculator!)
D = Inverse Tan (EF/DF)
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