1. Unit 3: Right Triangle Trigonometry
3.4 Solve Right Triangles

2. 3.4 Solve Right Triangles using
Trigonometric Ratios
Daily Agenda
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
Use the Pythagorean Theorem to Solve Right Triangles
Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
5 Question Daily Assessment
Daily Ticket out the Door
How will I show you that I’ve learned it?
solve
side lengths
angle
The length of two sides
The length of 1 side and 1 acute angle
The length of 1 side and 1 trigonometric ratio

3. 3.4 Solve Right Triangles using
Trigonometric Ratios
Daily Agenda
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
Use the Pythagorean Theorem to Solve Right Triangles
Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
5 Question Daily Assessment
Daily Ticket out the Door
How will I show you that I’ve learned it?
= 𝑥 2
= 𝑥 2
88.82= 𝑥 2
9.42
9.42=𝑥
9.4
tan − =∠𝑃
19˚
19.2°=∠𝑃
71˚
R = 90 – 19.2 = 70.8˚

4. 3.4 Solve Right Triangles using
Trigonometric Ratios
Daily Agenda
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
Use the Pythagorean Theorem to Solve Right Triangles
Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
5 Question Daily Assessment
Daily Ticket out the Door
How will I show you that I’ve learned it?
Example 2
sin 32° = 𝐵𝐶 7.4
3.92=𝐵𝐶
3.92
6.28
𝑥 = 7.4 2
6.28
𝑥 =54.76
3.92
𝑥 2 =39.39
𝑥=6.28
58˚
C = 90 – 32 = 58˚

5. 3.4 Solve Right Triangles using
Trigonometric Ratios
Daily Agenda
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
Use the Pythagorean Theorem to Solve Right Triangles
Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
5 Question Daily Assessment
Daily Ticket out the Door
How will I show you that I’ve learned it?
angle of elevation
angle of depression

6. 3.4 Solve Right Triangles using
Trigonometric Ratios
Daily Agenda
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
Use the Pythagorean Theorem to Solve Right Triangles
Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
5 Question Daily Assessment
Daily Ticket out the Door
How will I show you that I’ve learned it?
Example 3

7. 3.4 Solve Right Triangles using
Trigonometric Ratios
Daily Agenda
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
Use the Pythagorean Theorem to Solve Right Triangles
Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
5 Question Daily Assessment
Daily Ticket out the Door
How will I show you that I’ve learned it?
Example 4

8. 3.4 Solve Right Triangles using
Trigonometric Ratios
Daily Agenda
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
Use the Pythagorean Theorem to Solve Right Triangles
Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
5 Question Daily Assessment
Daily Ticket out the Door
How will I show you that I’ve learned it?
Example 5
618.7 ft

9. 3.4 Solve Right Triangles using
Trigonometric Ratios
Daily Agenda
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
Use the Pythagorean Theorem to Solve Right Triangles
Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
5 Question Daily Assessment
Daily Ticket out the Door
How will I show you that I’ve learned it?
Example 6 ft