All about right triangles Unit 8 - Trigonometry All about right triangles

angle Hyp H Opp Adj Adj Opp angle

SOH CAH TOA angle S 𝑂 𝐻 C 𝐴 𝐻 T 𝑂 𝐴 = 𝑂 𝐻 = 𝐴 𝐻 = 𝑂 𝐴 H O A 8 = 17 15

SOH CAH TOA angle angle S 𝑂 𝐻 C 𝐴 𝐻 T 𝑂 𝐴 = 𝑂 𝐻 = 𝑂 𝐻 = 𝐴 𝐻 = 𝐴 𝐻 = 𝑂 𝐴 = 𝑂 𝐻 = 𝐴 𝐻 = 𝑂 𝐴 angle 16 4 8 = = = 20 5 17 12 3 15 = = = 17 20 5 16 4 8 = = = 15 12 3

= 𝑂 𝐻 = 𝐴 𝐻 = 𝑂 𝐴 angle 24 12 = = 26 13 H 10 5 O = = 26 13 24 12 = =

= 𝑂 𝐻 = 𝐴 𝐻 = 𝑂 𝐴 24 12 = = 26 13 H 10 5 O = = 26 13 24 12 = = 10 5 angle A .731 .848 9.514 .73 .85 9.51

angle H S __OH A O _____ ___ = ___ sin 64 x 13

angle angle 38 64 = 1 T S _____ ___ = ___ tan 10 sin x _____ ___ = ___ __OA angle H H S O __OH A angle A O _____ ___ = ___ tan 38 10 sin 64 x _____ ___ = ___ x 1 13 13 sin 64 = x x = 11.68

angle angle 38 64 = 1 = 1 T S _____ ___ = ___ tan 10 sin x __OA angle H H S O __OH A angle A O _____ ___ = ___ tan 38 10 sin 64 x _____ ___ = ___ x x 1 tan 38 = 10 = 1 13 13 sin 64 x tan 38 x = 11.68 x = 10 / tan 38 x = 12.80

__AH C H O A angle _____ ___ = ___ 53 cos x 50

angle 56 angle 53 = 1 S C _____ ___ = ___ sin 15 x _____ ___ = ___ cos __OH S __AH C O H A O angle H _____ ___ = ___ sin 56 15 A angle x _____ ___ = ___ 53 cos x 50 50 cos 53 = x 1 x = 30.09

angle 56 = angle 1 53 = 1 S C sin _____ ___ = ___ 15 x x sin 56 15 sin __OH S __AH C O H A O angle H sin 56 _____ ___ = ___ 15 A = angle x x sin 56 15 1 sin _____ ___ = ___ 53 cos x 56 50 50 cos 53 = x 1 x = 30.09 x = 15 / sin 56 x = 18.09

H angle A __OH S O 60 _____ ___ = ___ sin x 25

angle angle 60 54 = 1 S S sin x _____ ___ = ___ sin 17 _____ ___ = ___ H angle H S A __OH A O __OH S O 60 54 sin x _____ ___ = ___ sin 17 _____ ___ = ___ sin = x x 25 25 60 1 x = 21.65

angle angle 60 54 = = 1 1 S S _____ ___ = ___ sin x _____ ___ = ___ H angle H S A __OH A __OH S O O 60 54 _____ ___ = ___ sin x _____ ___ = ___ sin 17 = x x x sin 54 = 17 25 25 sin 60 1 1 sin 54 x = 21.65 x = 17 / sin 54 x = 21.01