Summary
Highlights
The video begins by explaining how to identify a right-angled triangle by the square symbol indicating a 90-degree angle. It then details how to label the sides: the hypotenuse (H) is always opposite the right angle and is the longest side. The 'opposite' (O) and 'adjacent' (A) sides depend on which angle is being considered. The opposite side is across from the angle of interest, and the adjacent side is next to it.
The three main trigonometric equations are introduced: sin x = opposite/hypotenuse, cos x = adjacent/hypotenuse, and tan x = opposite/adjacent. To easily remember these, the mnemonic SOH CAH TOA is presented. SOH stands for Sine = Opposite/Hypotenuse, CAH for Cosine = Adjacent/Hypotenuse, and TOA for Tangent = Opposite/Adjacent.
In the first example, the goal is to find an unknown angle X. The first step is to label all sides (hypotenuse, opposite, adjacent) relative to angle X. Given the lengths of the opposite (15) and adjacent (11) sides, the TOA equation (tan x = opposite/adjacent) is selected. To solve for X, the inverse tan function (tan⁻¹) is used, resulting in X = tan⁻¹(15/11), which calculates to 53.7 degrees.
The second example demonstrates finding the length of an unknown side, PQ (which is the hypotenuse). The sides are labeled, and the known angle is 35 degrees. The adjacent side is 20 cm, and the opposite side is irrelevant in this case. The CAH equation (cos x = adjacent/hypotenuse) is chosen. The equation is then rearranged to solve for the hypotenuse: Hypotenuse = Adjacent / cos x. Plugging in the values, the hypotenuse is calculated as 20 / cos(35), which is 24 cm. A reminder is given to close brackets after the angle on calculators to avoid errors.