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Intro to Trig

Trigonometry starts with side ratios in a right triangle... it gets more involved later. With respect to the angle (acute) of reference, you need to identify the hypotenuse, and the opposite and adjacent sides and form fractions representing the Sine, Cosine and Tangent of that angle. Basic Notes... What do we know about triangles? 3 sides, 3 angles. Three angles add up to 180 degrees Longest side opposite biggest angle Shortest side opposite smallest angle Medium opposite to medium. Opposite side is the one not connected The other two are called adjacent. Right Triangles A triangle with a 90 degree angle is called a right triangle. Side opposite to 90 is the longest side… aka hypotenuse Note: the other 2 angles are both acute (less than 90) and add up to 90 (complementary angles). If a triangle has an angle more than 90 degrees, it’s called an obtuse triangle. In a right triangle, the square of the hypotenuse is equal to to the sum of the squares of the other two sides: a2 + b2 = c2 (Pythag). This is about sides, not angles. BUT… there is a connection between sides and angles, and this is what we call Trigonometry. tri = 3 gon = corner metry = measure Right Triangle Trigonometry Using an acute angle as point of reference (we’ll use point A) we can identify the opposite side and the adjacent sides. One of the adjacent sides is the hypotenuse. Using the abbreviations opp, hyp and adj, we label the three sides. The 3 fractions formed with pairs of side lengths are called trigonometric ratios, and are named sine, cosine and tangent. sin(A) = opp/hyp cos(A) = adj/hyp tan(A) = opp/adj So what? These ratios for any angle are known values in your calculator (before calculators, the values were printed in tables). Using these values, we can find missing side lengths or angles, by setting up and solving proportions.