Download Applying TRIG Ratios Pt. I PPT

10/20: Apply trig ratios to find missing side lengths of right
triangles
Do Now
Agenda
On your desk:
DO NOW! & Check
- Pencil & Calculator
-Today’s Handouts
Homework
Handout
(8 problems)
Guided Practice
Independent
Practice
DO NOW!
Homework!
(maybe…)
Parent-Teacher
Conferences
TONIGHT!
3PM – 9PM!
We will learn to…
• Apply trig ratios to find missing side lengths of
right triangles.
Trigonometric Ratios Review:
Sine Ratio:
sin  =
Cosine Ratio: cos  =
Tangent Ratio: tan  =
opposite
hypotenuse
adjacent
hypotenuse
hypotenuse
opposite

opposite
adjacent
adjacent
A pneumonic to help remember trig ratios is…
SOH CAH TOA
Example 1: Find the value of x. Round to tenth.
Given:
Right Triangle
Opposite Side = 11
Angle = 32⁰
Finding:
Adjacent Side = x
Trig Ratio:
Tangent
Write Equation, Substitute, & Solve:
tan  =
opposite
adjacent
11
x  tan 32° =
x
x
x tan 32° = 11
tan 32° tan 32°
11
x =
tan 32°
x ≈ 17.6 units
Example 2: Use your value of x to find the area of
the triangle above. Round to the nearest whole unit.
Area of Triangle = bh or
2
17.6
A = 17.6(11)
2
A ≈ 97 units
𝟏
bh
𝟐
b = base
h = height
Example 3: Find the value of x and then y. Round to hundredth.
12.08
a2 + b2 = c2
12.082 + y2 = 162
y2
= 110.07
y ≈ 10.49
Given:
Solve:
opposite
How
else could we have
- Right
Triangle
sin  =
solved for y after finding
hypotenuse
- Hypotenuse
= 16of x?
the value
x
sin
49°
=
16
 16
- Angle = 49⁰
16
16 sin 49° = x
Finding:
- Opposite Side = x
- Adjacent Side = y
Trig Ratio:
- Sine (for x)
- Cosine (for y)
x ≈ 12.08 units
cos  =
adjacent
hypotenuse
y
cos
49°
=
16
 16
16
16 cos 49° = y
y ≈ 10.50 units