In a right-angled triangle, the sides and the angles are connected by three trigonometric ratios.

The three trig ratios are:

A quick way to remember this is to memorise the word

SOHCAHTOA

In this worksheet, you will be told to give your answers to 3 significant figures (3sf). You also don't need to worry about the units for these questions.

**Example 1**

Using trigonometry, calculate the side length* x* to 3 sig. figs.

**Answer**

Label the sides adjacent, opposite and hypotenuse in relation to the given angle 34º.

The given sides are the opposite (x) and the hypotenuse (8).

**SOH**CAHTOA

The correct trig ratio is **SIN**.

Set up the trig equation to get:

sin34º = *x*/8

*x*/8 = sin34º

*x* = 8 sin34º

*x* = 8 x 0.559192903....

**x**** =** **4.47 **(3 s.f.)

**Example 2**

Using trigonometry, calculate the side length* x* to 3 sig. figs.

**Answer**

Label the sides adjacent, opposite and hypotenuse in relation to the given angle 54º.

The given sides are the hypotenuse (x) and the adjacent (7).

SOH**CAH**TOA

The correct trig ratio is **COS**.

Set up the trig equation to get:

cos54º = 7/*x*

*x*cos54º = 7

*x* = 7/cos54º

*x* = 7 ÷ 0.587785252....

**x**** =** **11.9 **(3 s.f.)

**Example 3**

Using trigonometry, calculate the angle θº to 3 sig. figs.

**Answer**

Label the sides adjacent, opposite and hypotenuse in relation to the angle θº.

The given sides are the adjacent and the hypotenuse.

SOH**CAH**TOA

The correct trig ratio is **COS**.

Set up the trig equation to get:

cos θ = 3/5 = 3 ÷ 5 = 0.6

θ = cos^{-1} (0.6)

**θ =** **53.1º **(3 s.f.)