similarity of any right triangle with the same acute measure. all 3 of the triangles are similar...
TRANSCRIPT
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)