Using the

Cosine Rule on the triangle ACF produces:

From figure 1 and the

cosine rule it can be shown that

The solution with the help of the cosine rule and the calculus

This angle can be expressed by the cosine rule in the triangle ABC.

In the case where consideration of the problem is not feasible as a whole, then different elements of this problem and its solutions can be used for studying and repetition of the following concepts and skills: the sine rule, the cosine rule, applications of the derivative, the arithmetic mean and geometric mean, the tangent and the secant, the exterior angle of a triangle, the inscribed angle, and others (ACARA, 2012).

Since Pythagoras1 Rule and the

Cosine Rule are in various mathematics curricula at either Year 10 or Year 11 (eg, ACARA, 201 la; VCAA, 2005b), finding the tetrahedral angle can be used in mathematics as an example of applying mathematics outside the mathematics classroom (ACARA, 2011a).

There are three basic trig rules: the sine rule,

cosine rule, and tangent rule.

[m.sup.2] + [q.sup.2] = [AD.sup.2] = 2[r.sup.2](1 - cos [alpha]) (Pythagoras' theorem and the

cosine rule) [n.sup.2] + [p.sup.2] = [BC.sup.2] = 2[r.sup.2](1 - cos [beta]) (Pythagoras' theorem and the

cosine rule)

There are three trig formulas we will use, sine rule,

cosine rule, and tangent rule.

There are three basic trig rules, the sine rule, the cosine rule, and the tangent rule.

Cosine rule cosine of angle = adjacent / hypotenuse (CAH)