Right-Angled Trigonometry

If we have right-angled triangle, we can use sine, cosine and tangent functions to find length of sides and angles easily.

A right-angled triangled triangle consists of 3 sides. These are the hypotenuse, opposite and adjacent. (Fig. 1)

The ypotenuse is the longest side of the triangle. It can be looked at as diagonal side. The opposite is the side opposite to the angle given. Keep in mind that this angle cannot be the 90° of the right angled triangle. It has to be a different angle. (Fig. 1)

Anjacent is the side that is right next to the angle (not the hypotenuse). It is very important to identify the sides correctly, as if it isn't, the results will differ!

• The sin θ (read as sine of theta (angle)) is equal to the opposite divided by the hypotenuse (o/h)

• The cos θ (read as cosine of tetha (angle)) is equal to the adjacent divided by the hypotenuse (a/h)

• The tan θ  (read as tangent of tetha (angle)) is equal to the opposite divided by the adjacent (o/a)

In short, you can memorize this as the following to make it easier

Soh Cah Toa (Fig. 2)

To find a certain angle of a right angled triangle, you will need to use the inverse of sin, cos, tan, in other words: sin^-1(o/h), cos^-1(a/h), tan^-1(o/a). Depending on your needs, you will choose one of these.

Find side x (fig. 3)

First, let us identify what sides we are working with. X is next to the angle of 30° , so that is our adjacent. The hypotenuse of this triangle is given to be 50 cm. So we have our opposite and adjacent. Therefore looking at soh cah toa, we need to use the tan function. 

We know that tan = o/a. We need to rearrange this so we can solve for the adjacent. Therefore we will get the new formula x = tan 30 × 50. Enter this in your GDC, and the approximate value of x will be: 28.87 cm. If you didn't get this answer, make sure your calculator is set to degree and not radians.

Find angle θ. (fig. 4) 

In this example we are working with sides hypotenuse (40 cm) and opposite (20 cm). Hence, we will need to use sin^-1 to find the angle. In your calculator, type sin^-1  (20/40). This will give the value of angle θ as 30°.