Calculate the length of side AB (opposite) in a right angled triangle, where angle C is 32 degrees and length of BC (hypotenuse) is 8cm.

First, we can draw a diagram to visualise the triangle and the elements of the question. Looking at this, we can see that we know the length of the hypotenuse (H) and we need to calculate the length of the opposite (O) side, AB. Therefore, from the trigonometric ratios, we need to choose the ratio involving the letters O and H which is the sine ratio: SOH.Sin(x) = opposite/hypotenuse Inputting the information from the question… sin(32) = AB/8 8 x sin(32) = AB (Multiply both sides by 8 to isolate the opposite side as the subject)AB = 4.2 cm