Transcript Trigonometric Ratios

Trigonometric Ratios
Set up and Solve for missing sides
and angles
SOH CAH TOA
Trig Ratios and Right Triangles
The sides of the triangle have names, but it
depends on the angle you are looking from.
From angle A –
Blue
From angle B –
Red
Describing the Sides
• Opposite side in relationship to angle using
Across from the angle, does not touch the
angle we are using
• Adjacent side in relationship to angle using
Touches the angle, not hypotenuse, connects
angle to right angle
• Hypotenuse
Always the longest side, across from the right
angle
Trig Ratios
The trigonometric value of an angle is related to
a specific ratio of two of the sides of the triangle
SOH
CAH
TOA
opp
sin e  sin  
hyp
adj
cos ine  cos  
hyp
op
tan gent  tan  
adj
Set up
1. Determine Trig ratio you are using - You need to know
what angle you are given or need to find, then know
what sides you are using in relationship to that angle
2. Set up trig ratio
3. Solve trig ratio
1. If unknown is in numerator then trig value of angle times
denom
2. If unknown is in denominator then numerator divided by
trig value of angle
3. If angle is unknown then inverse trig value of the ratio of
sides
Examples
Examples Continued
Problem Solving
Angle of Depression – angle line forms with
horizon, coming down
Angle of Elevation – angle formed with horizon
going up
Example Continued
• When an 18 ft ladder is leaning against a wall
and it makes a 68 degree angle with the
ground. How high up the wall does the ladder
reach?
Homework
Due 4/10 or 4/11 depending on class
Pg 644 4-22 even
Pg 648 1-9 odd 10,11,12
Honors Magic Square pg 607 Due 4/14 4/15
depending on class