Right Angle Trigonometry

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Right Angle Trigonometry

Labeling a Right Triangle In trigonometry, we give each side a name according to its position in relation to any given angle in the triangle: Hypotenuse, Opposite, Adjacent  Hypotenuse Adjacent Opposite The _________ is always the longest side of the triangle. The _________ side is the leg directly across from the angle. The _________ side is the leg alongside the angle. hypotenuse opposite adjacent

Trigonometric Ratios We define the 3 trigonometric ratios in terms of fractions of sides of right angled triangles.    Hypotenuse (HYP) Adjacent (ADJ) Opposite (OPP)

SohCahToa S ine equals Opposite over H ypotenuseC osine equals Adjacent over HypotenuseTangent equals O pposite over Adjacent

Practice Together: Given each triangle, write the ratio that could be used to find x by connecting the angle and sides given. 65 a x Find x. 32 b x

YOU DO: Given the triangle, write all the ratios that could be used to find x by connecting the angle and sides given. 56 d x Find x. c

In a right triangle, if we are given another angle and a side we can find: The third angle of the right triangle: How? The other sides of the right triangle: How? Using the ‘angle sum of a triangle is 180’ Using the trig ratios

Steps to finding the missing sides of a right triangle using trigonometric ratios: Redraw the figure and mark on it HYP , OPP , ADJ relative to the given angle 61 9.6 cm x HYP OPP ADJ

Steps to finding the missing sides of a right triangle using trigonometric ratios: For the given angle choose the correct trigonometric ratio which can be used to set up an equation Set up the equation 61 9.6 cm x HYP OPP ADJ    

Steps to finding the missing sides of a right triangle using trigonometric ratios: Solve the equation to find the unknown. 61 9.6 cm x HYP OPP ADJ      

Practice Together: Find, to 2 decimal places, the unknown length in the triangle. 41 x m 7.8 m

YOU DO: Find, to 1 decimal place, all the unknown angles and sides in the triangle.  a m 14.6 m 63 b m

Steps to finding the missing angle of a right triangle using trigonometric ratios: Redraw the figure and mark on it HYP , OPP , ADJ relative to the unknown angle  5.92 km HYP OPP ADJ 2.67 km

Steps to finding the missing angle of a right triangle using trigonometric ratios: For the unknown angle choose the correct trig ratio which can be used to set up an equation Set up the equation      5.92 km HYP OPP ADJ 2.67 km

Steps to finding the missing angle of a right triangle using trigonometric ratios: Solve the equation to find the unknown using the inverse of trigonometric ratio.        5.92 km HYP OPP ADJ 2.67 km

Practice Together: Find, to one decimal place, the unknown angle in the triangle.  3.1 km 2.1 km

YOU DO: Find, to 1 decimal place, the unknown angle in the given triangle.  7 m 4 m

Practice: Isosceles Triangles Using what we already know about right angles in isosceles triangles find the unknown side. 10 cm x cm 67 

YOU DO: Isosceles Triangles Find the unknown angle of the isosceles triangle using what you already know about right angles in isosceles triangles. 8.3 m 5.2 m 

Practice: Circle Problems Use what you already know about right angles in circle problems to find the unknown angle. 6 cm 10 cm 

YOU DO: Circle Problems Use what you already know about right angles in circle problems to find the unknown side length. 6.5 cm 56  x cm

Practice: Other Figures (Trapezoid) Find x given: 10 cm x cm 65  48

YOU DO: Other Figures (Rhombus) A rhombus has diagonals of length 10 cm and 6 cm respectively. Find the smaller angle of the rhombus. 10 cm 6 cm 