Trig Ratios in a Right Triangle

In a right triangle, $\sin\theta = \frac{\text{opp}}{\text{hyp}}$, $\cos\theta = \frac{\text{adj}}{\text{hyp}}$, $\tan\theta = \frac{\text{opp}}{\text{adj}}$. Their reciprocals are cosec, sec and cot. The hypotenuse comes from Pythagoras: $\text{hyp} = \sqrt{\text{opp}^2 + \text{adj}^2}$.

Set the opposite and adjacent legs. The lab computes the hypotenuse and all six ratios as decimals and as fractions. Try opp = 3, adj = 4 to see hyp = 5 with sin = 0.6, cos = 0.8.

Students confuse 'opposite' and 'adjacent' with respect to the angle. The opposite side faces $\theta$; the adjacent side touches it but is not the hypotenuse. Label your triangle before writing ratios.

A ladder leaning on a wall forms a right triangle; knowing the angle tells you how high it reaches. A kite string makes a right triangle with the ground - trig predicts the kite's height from the string length and angle.