Pythagoras, Trigonometry and Coordinate Geometry: Where to start

A ladder leaning on a wall. A kite on a tight string. A wire run from one corner of a box to the far corner opposite. Each one hides a triangle. Find the triangle, see what you already know about it, and the right tool follows. That is the whole chapter in one habit. So this video points you at the tool you need, and the place to begin.

The list on your screen runs in order. It starts with flat triangles that have a right angle, then triangles without one, then triangles hidden inside solid shapes. Work on a coordinate grid has its own chapter, on coordinates and straight-line graphs.

If right-angled triangles are new to you, start with Pythagoras' theorem in two dimensions. A common slip is adding or taking away the sides without squaring them first. Once Pythagoras feels solid, go to Trigonometric ratios: labelling sides and choosing sin, cos or tan. Label every triangle with opposite, adjacent and hypotenuse before you choose a ratio. Using trigonometry to find missing sides and angles puts those ratios to work. Plenty of students reach for Pythagoras or the area when the question needs trigonometry, and that video shows how to tell. Angles of elevation and depression takes those ratios outside, to towers, cliffs and boats. It is about measuring the angle from the right horizontal line. If you sit Foundation, that is where your part of the chapter ends. Everything after it is Higher work. If you sit Higher and right-angled trigonometry already feels comfortable, start at The sine rule and the area of a triangle. A popular mistake is treating the triangle as right-angled when it is not. Trigonometric ratios of obtuse angles is a short Higher step that few courses set, so check your own specification before you spend time on it. The cosine rule comes next. Students often write it down wrong, so the video spends its time on putting the numbers in and rearranging it for an angle. If solid shapes are what worry you, start at Pythagoras' theorem in three dimensions. Some students take a length off the diagram instead of working it out. Those answers earn one mark at most. Finding lengths in 3D using Pythagoras and trigonometry chains the two tools together. Marks go on rounding too early, so carry every value unrounded to the end. Finding the angle between a line and a plane asks you to draw one line that is not on the diagram yet. Only then is there a triangle to work with. Trigonometry in 3D and complex figures closes the chapter. Many students leave this kind of question out altogether. Yet every tool it needs is taught earlier in this list. Each video can be found by searching its name, or the code beside it. The quickest way is the scholafly.com website, which indexes every video in every subject. If you are not sure where you stand, begin at the top, with the theorem every other video leans on.

Next in the chapter is Pythagoras' theorem in two dimensions. Hopefully that's next in your feed, but if not, search for ScholaFly M A thirty, oh one.

Every other video is on scholafly.com too, easy to search by video code or by keyword. Whatever you're revising, go there and have a look, or, watch the next video.