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9.5
Trig Ratios
HMWK: p. 562, #s 13-37 odd, 38, 39
Game Plan: Today I will be able to use Trig Ratios to
determine side lengths of triangles.
Warm-up: Solve for the missing length.
9.5
Trig Ratios
Applications ~ Special Rt. 
The roof of a doghouse is shaped like an
equilateral triangle with height 3 feet.
Estimate the area of the cross-section
of the roof.
Steps
3 ft
1. Use spec. tri.
relationships to find
base of triangle
2. Use area formula
5.2 ft.
Trig Ratios
Origin of SOH CAH TOA
9.5
Trig Ratios
Trig Ratios
Trigonometry – Greek for “measure of
triangles”
Trig Ratios – ratio of lengths of sides of rt.
triangle



Uses acute angles
Basic trig ratios




Sine (sin)
Cosine (cos)
Tangent (tan)
9.5
Trig Ratios
SOH CAH TOA
SOH
OPP
sin 
HYP
B
CAH
cos 
ADJ
HYP
TOA
OPP
tan 
ADJ
42°
C
A
9.5
Trig Ratios
Using Trig Ratios ~ Sides
SOH CAH TOA
B
OPP 3
sin A 
  .6000
HYP 5
a=3
ADJ 4
cos A 
  .8000
HYP 5
c=5
46°
C
b=4
A
tan A 
OPP 3
  .7500
ADJ 4
Round to 4 decimals places!
Find trig ratios for angle B.
9.5
Trig Ratios
Using Trig Ratios ~ Angles

Make sure calculator is in DEGREE
mode

“MODE” and check 3rd line down
Use calculators to find following
measures.
1. sin37°
2. cos37°
3. tan37°
9.5
Trig Ratios
Trig Ratios ~ Angles
B
Sketch the given right triangle ABC, if
mA=46°, mC=90° and a=7. Find
the length of sides b and c.
7
SOH CAH TOA
c
1. Set up all trig ratios
2. Determine which
ratio to use
46°
C
b
A
3. Solve for variable
9.5
Trig Ratios
Applications
You are measuring the height of a building. You
stand 100 feet from the base of the building. You
measure the angle of elevation from a point on
the ground to the top of the building to be 48°.
Estimate the height of the building.
Be sure to …
• sketch the problem
• label the problem
• SOH CAH TOA
9.5
Trig Ratios
Inverse Trig Ratios


Used to find angle measures of right
triangles.
Sin-1, cos –1 , tan –1
9.5
Trig Ratios
Wrap-Up
Right Triangles …
 Altitude
 Geometric Mean
 Pythagorean Thm
 Converse of Pyth Thm
 Special Right Triangles
 Trig Ratios