1. 8.2 Trigonometric Ratios

2. Trigonometric Ratios
Trigonometric Ratios- is a ratio of two sides of a right triangle.
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

3. Trigonometric Ratios
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

4. Examples:
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
sin J
cos J
tan K
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

5. Examples:
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
cos A
tan B
sin B
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

6. Examples:
Use your calculator to find each trigonometric ratio. Round to the nearest hundredth.
sin 52°
cos 19°
tan 65°
tan 11°
sin 62°
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

7. Examples: Find each length. Round to the nearest hundredth. BC QR
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

8. Examples: Find each length. Round to the nearest hundredth. FD DF
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

9. Examples: Find each length. Round to the nearest hundredth. ST BC
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

10. Examples: Find each length. Round to the nearest hundredth. JL
CB and AC
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

11. Examples:
Find AC, the length of the ramp, to the nearest hundredth of a foot. Angle C= 4.8o, AB=1.2 ft
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…

12. Examples:
The Pilatusbahn in Switzerland is the world’s steepest cog railway. Its steepest section makes an angle of about 25.6º with the horizontal and rises about 0.9 km. To the nearest hundredth of a kilometer, how long is this section of the railway track?
By AA Similarity, all of these triangles are similar. Therefore, ΔABC~ΔDEF~ΔXYZ…
0.9 km