Capítulo IX · Neste capítulo você vai
Right triangles
- use the notation of the elements of a triangle and recognize the hypotenuse and legs;
- demonstrate the metric relations of the right triangle, including the Pythagorean theorem;
- prove that the sine, cosine and tangent of an acute angle are ratios between sides;
- solve a right triangle — calculate all sides and angles — from two data;
- apply all this to problems of heights and distances.
Until now, sine, cosine and tangent have lived in the trigonometric cycle. In this chapter they return to their origin: the right triangle. Once an acute angle is fixed, the ratio between two sides does not depend on the size of the triangle — and this is what makes it possible to measure the height of a building, the width of a river or the distance to a tower without climbing or crossing anything.