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 ID: 763955
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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