1. Warm Up
Solve for each missing side length. x 6 12
30° 8 x 26 10

2. Homework 5-1
ft ft. 3. No ( ≠ 43 2 ) ft Runners more frequently try to steal 2nd because it is farther from home than 3rd.

3. Homework 5-2
1. 𝑎=4, 𝑏= x=y= 𝑦= , 𝑥=3 4. y=3 2 , 𝑥=6 5. 𝑥=𝑦= 𝑥=𝑦= 𝑦=8, 𝑥= 𝑣=2 3 , 𝑢=4

4. Theta (𝜃) represents an unknown angle.
Notes
Theta (𝜃) represents an unknown angle.
Across from right angle
Forms one side of angle theta.
Hypotenuse
Opposite
Across from theta 𝜃
Adjacent
Forms other side of theta
Adjacent means “next to”

5. Sine: sin 𝜃 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Notes
Right triangle trig:
Sine: sin 𝜃 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Cosine: cos 𝜃 = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Tangent: tan 𝜃 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
We can easily remember these with the acronym SOH CAH TOA.
Hypotenuse
Opposite 𝜃
Adjacent

6. When you have a right triangle with a known side and one other known:
When you have a right triangle with a known side length and one other part:
When you have a right triangle with a known side and another angle or side:
SOHCAHTOA!

7. Activity

8. Notes
In this triangle, which side is opposite, adjacent, and hypotenuse based on angle C? C
Opposite = B
Adjacent =
Hypotenuse = A

9. Notes
In this triangle, which side is opposite, adjacent, and hypotenuse based on angle L? L D A
Opposite =
Adjacent =
Hypotenuse =

10. Notes – You try!
In this triangle, which side is opposite, adjacent, and hypotenuse based on angle M? M D A
Opposite =
Adjacent =
Hypotenuse =

11. Notes Is this a right triangle
Notes Is this a right triangle? Trig functions only work on right triangles!! 15 8 17
Find tan 𝑥 = sin 𝑥 = cos 𝑥 = x

12. Notes
Label each leg opposite, adjacent or hypotenuse. Write the formula for n and solve to the nearest tenth. C 𝑛 B 13
40° A

13. Notes
Label each leg opposite, adjacent or hypotenuse. Write the formula for y and solve to the nearest tenth. Q
82° 𝑦 4 P R

14. Notes
Label each leg opposite, adjacent or hypotenuse. Write the formula for x and solve to the nearest tenth. O 5 𝑥 H
24° T

15. Notes – You try!
Label each leg opposite, adjacent or hypotenuse. Write the formula for n and solve to the nearest tenth. B
39° 6 𝑛 A G

16. Notes – You try!
Label each leg opposite, adjacent or hypotenuse. Write the formula for y and solve to the nearest tenth. R 𝑦
30° A 10 D

17. Notes – You try!
Label each leg opposite, adjacent or hypotenuse. Write the formula for x and solve to the nearest tenth. B 14 A
72° 𝑥 C