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Learn
More - FAQs
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Now!
In this section of the
, we will be looking at SOHCAHTOA and the sine and cosine rules, as well as taking a look at the tangent function. But before you dive in you need to know that sines, cosines and tangents of angles are just functions on the angles. There should be sin, cos and tan buttons on your calculator (sin, cos and tan are shorthand). Now that you know that, let's look at:
In a right angled triangle we can use what we call SOHCAHTOA to find lengths (by rearranging the equations below), and angles. SOHCAHTOA stands for "Sine: Opposite, Hypotenuse, Cosine: Adjacent, Hypotenuse, Tangent: Opposite, Adjacent". The words like Opposite and Adjacent refer to the angle, i.e. the opposite side to the angle, the side that's adjacent to the angle. Here are word equations stating what each piece of the SOHCAHTOA means. In case you don't know what hypotenuse means, it's the side of the triangle opposite the right angle.
SOH
Sine of an angle = Side of triangle Opposite to angle divided by the Hypotenuse of the triangle.
CAH
Cosine of an angle = Side of triangle Adjacent to angle divided by the Hypotenuse of the triangle.
TOA
Tangent of an angle = Side of triangle Opposite to angle divided by side of triangle Adjacent to angle.
In the following diagram find angle A:
Angle A is opposite to side a. The hypotenuse is c, so, by using SOHCAHTOA we would use the sine function.
sin A = 5 divided by 10 cm = 0.5 cm
A = sin
0.5 = 30 degrees. How did we end up with this? We take the inverse sine of sin A, which gives us A. However, we have to take the inverse (sin
A = sin
A = 30
, as said above.
In the following diagram, calculate the length of the side adjacent to angle A:
Angle A is opposite to side a. The hypotenuse isn't mentioned, so use the tangent function.
Tan 60 degrees = 10 divided by the length of the adjacent side.
Therefore the adjacent side length = 10 divided by 1.73.= 5.77 cm to 2.d.p.
...........................................
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