Oblique Triangles in Applications

Having just looked at how to solve oblique triangles, let’s look at a couple “word problems” (applications) involving such triangles. We’ll be using the Law of Sines, and also exploring alternative methods of solution. A tilted tree Let’s start with this real application from 1999: Will the Tree Hit the House? There is a tree …

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Proving the Law of Cosines

Last week we looked at several proofs of the Law of Sines. Here we will see a couple proofs of the Law of Cosines; they are more or less equivalent, but take different perspectives – even one from before trigonometry and algebra were invented! Proof using coordinates First, here is a question we looked at …

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Proving the Law of Sines

Two of the most useful facts in trigonometry are the Law of Sines and the Law of Cosines (sometimes called the Sine Rule or Sine Formula, and the Cosine Rule or Cosine Formula). Over the years we were often asked where they come from (or are just asked about them, and reflexively offer proofs). There …

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Area of Pyramids and Cones

We’ve looked at the volume of a pyramid, the formula for which can be found geometrically by a couple very different methods. Cones can be handled the same way, so we can skim over them. Let’s finish up by considering the surface areas of both cones and pyramids. Volumes and areas I’ll start with a …

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