BASIC GEOMETRY Section 8.2: Trigonometric Ratios

Similarity of any right triangle with the same acute measure. All 3 of the triangles are similar Their sides are in proportion We can write these proportions differently

SOHCAHTOA Trig Ratios Sine of an angle = Cosine of an angle = Tangent of an angle = hypotenuse opposite adjacent SOHCAHTOA

EXAMPLE 1: Write each trig ratio as a fraction and as a decimal rounded to the nearest hundredth. Sin J Cos J Tan K Sin K

Special Right Triangles 30-60-90 45-45-90 60˚ 45˚ 30˚ 45˚ Sin 30 = Cos 30 = Tan 30 = Sin 60 = Cos 60 = Tan 60 = Sin 45 = Cos 45 = Tan 45 =

Calculating Trig Ratios Use your calculator to find each trig ratio. Round to the nearest hundredth. (MAKE SURE YOU ARE IN DEGREES) A) Sin 52˚ B) Cos 19˚ C) Tan 65˚

Sine & Cosine Properties Sin & Cos of an angles is always less than _____

Solving Trig Equations to Find Missing Lengths Find BC to the nearest hundredth. Draw your picture Set up a Trig ratio using what you have and what you need. Cross multiply Solve

Find QR to the nearest hundredth.

Find FD to the nearest hundredth

The Pilatusbahn in Switzerland is the world’s steepest cog railway The Pilatusbahn in Switzerland is the world’s steepest cog railway. Its steepest section makes an angle of about 25.6˚ with the horizontal and rises about 0.9 km. To the nearest hundredth of a kilometer, how long is this section of the railway track?

Assignment #2 Page 529 #’s 1-21,(82)