Similarity of any right triangle with the same acute measure.All 3 of the triangles

are similarTheir sides are in

proportion

We can write these proportions differently

Trig RatiosSine of an angle =

Cosine of an angle =

Tangent of an angle =

Opposite

Hypotenuse

Adjacent

Hypotenuse

Opposite

Adjacent

adjacent

opposite

hypotenuse

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

b) Cos J

c) Tan K

d) Sin K

Special Right Triangles30-60-90 45-45-90

30˚

60˚

45˚

45˚

Sin 30 =Cos 30 =Tan 30 =

Sin 60 = Cos 60 = Tan 60 =

Sin 45 =Cos 45 =Tan 45 =

Calculating Trig RatiosUse 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 PropertiesSin & Cos of an angles is always less than

_____

Solving Trig Equations to Find Missing Lengths

1) Draw your picture

2) Set up a Trig ratio using what you have and what you need.

3) Cross multiply4) Solve

Find BC to the nearest hundredth.

Find QR to the nearest hundredth.

Find FD to the nearest hundredth

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 #2Page 529 #’s 1-21,(82)