1. Parent-Teacher Conferences TONIGHT!
10/20: Apply trig ratios to find missing side lengths of right triangles
Do Now
On your desk:
- Pencil & Calculator
-Today’s Handouts
DO NOW!
Agenda
DO NOW! & Check
Guided Practice
Independent Practice
Homework! (maybe…)
Homework
Handout
(8 problems)
Parent-Teacher Conferences TONIGHT!
3PM – 9PM!

3. We will learn to…
Apply trig ratios to find missing side lengths of right triangles.

4. SOH CAH TOA A pneumonic to help remember trig ratios is…
Trigonometric Ratios Review:
opposite
hypotenuse
Sine Ratio:
sin  = 
opposite
hypotenuse
adjacent
adjacent
hypotenuse
Cosine Ratio:
cos  =
opposite
adjacent
Tangent Ratio:
tan  =
A pneumonic to help remember trig ratios is…
SOH
CAH
TOA

5. Example 1: Find the value of x. Round to tenth.
Given:
Write Equation, Substitute, & Solve:
Right Triangle
tan  =
opposite
adjacent
Opposite Side = 11 11 x
x   x
tan 32° =
Angle = 32⁰
x tan 32° = 11
Finding:
Adjacent Side = x
tan 32°
tan 32°
x = 11
tan 32°
Trig Ratio:
Tangent
x ≈ units

6. Example 2: Use your value of x to find the area of the triangle above
Example 2: Use your value of x to find the area of the triangle above. Round to the nearest whole unit.
Area of Triangle = or bh 2
𝟏 𝟐 bh
b = base
h = height
A = 17.6(11) 2
17.6
A ≈ 97 units

7. How else could we have solved for y after finding the value of x?
Example 3: Find the value of x and then y. Round to hundredth.
Given:
Solve:
How else could we have solved for y after finding the value of x?
sin  =
opposite
hypotenuse
- Right Triangle
- Hypotenuse = 16 x 16
16  16
sin 49° =
- Angle = 49⁰
12.08
16 sin 49° = x
Finding:
a2 + b2 = c2
x ≈ units
- Opposite Side = x
y2 = 162
cos  =
adjacent
hypotenuse
- Adjacent Side = y
y2 =
Trig Ratio: y 16
y ≈ 10.49
- Sine (for x)
16  16
cos 49° =
- Cosine (for y)
16 cos 49° = y
y ≈ units