Right Angled Trigonometry Labeling a Right Triangle trigonometry

Right Angled Trigonometry

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

Trigonometric Ratios Adjacent (ADJ) We define the 3 trigonometric ratios in terms of fractions of sides of right angled triangles. Hy po ten use (HY P) Opposite (OPP)

Soh. Cah. Toa Sine equals Opposite over Hypotenuse Cosine equals Adjacent over Hypotenuse Tangent equals Opposite over Adjacent

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

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

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

Steps to finding the missing sides of a right triangle using trigonometric ratios: HYP 61 9. 6 cm ADJ x OPP 1. Redraw the figure and mark on it HYP, OPP, ADJ relative to the given angle

Steps to finding the missing sides of a right triangle using trigonometric ratios: 2. For the given angle choose the correct trigonometric ratio which can be used to set up an equation 3. Set up the equation HYP 61 9. 6 cm ADJ x OPP

Steps to finding the missing sides of a right triangle using trigonometric ratios: 4. HYP 61 9. 6 cm ADJ x OPP Solve the equation to find the unknown.

7. 8 m xm 41 Practice Together: Find, to 2 decimal places, the unknown length in the triangle.

14. 6 m YOU DO: bm am 63 Find, to 1 decimal place, all the unknown angles and sides in the triangle.

Steps to finding the missing angle of a right triangle using trigonometric ratios: OPP 1. 2 k HYP m 2. 67 km 5. 9 ADJ Redraw the figure and mark on it HYP, OPP, ADJ relative to the unknown angle

Steps to finding the missing angle of a right triangle using trigonometric ratios: 2. For the unknown angle choose the correct trig ratio which can be used to set up an equation 3. Set up the equation OPP 2 k HYP m 2. 67 km 5. 9 ADJ

Steps to finding the missing angle of a right triangle using trigonometric ratios: 4. OPP HYP 2. 67 km 5. 9 2 k m ADJ Solve the equation to find the unknown using the inverse of trigonometric ratio.

Practice Together: 3. 1 km 2. 1 km Find, to one decimal place, the unknown angle in the triangle.

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

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

YOU DO: Isosceles Triangles Find the unknown angle of the isosceles triangle using what you already know about right angles in isosceles triangles. 5. 2 m 8. 3 m

Practice: Circle Problems Use what you already know about right angles in circle problems to find the unknown angle. 10 6 cm 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 c m m xc 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. 6 cm 1 m c 0