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Lesson 13.1 Right Triangle Trigonometry Adjacent Leg SOH opp sin hyp hyp 1 csc opp sin CAH adj cos hyp hyp 1 sec adj cos TOA opp tan adj cot adj 1 opp tan Finding Exact Values 30-60-90 60° 2 1 30° 3 sin 30 1 2 3 cos 30 2 tan 30 1 3 3 3 3 sin 60 2 1 cos 60 2 tan 60 3 Finding Exact Values 1 45° 45-45-90 2 2 45° 2 45° 45° 1 2 sin 45 2 2 2 cos 45 2 tan 45 2 1 2 Example 1 Find Trigonometric Values [A] 3 5 4 4 sin 5 5 csc 4 3 cos 5 5 sec 3 4 tan 3 3 cot 4 Example 1 Find Trigonometric Values [B] 13 5 12 5 sin 13 13 csc 5 12 cos 13 13 sec 12 5 tan 12 12 cot 5 Example 2 [A] Use one Trig Ratio to find others 2 cos 5 cot ? Example 2 [B] Use one Trig Ratio to find others 5 tan 3 sec ? 34 3 hyp 34 sec adj 3 32 5 2 h 2 34 h 2 h 34 5 Example 3 Find missing sides of Right Triangles Calculator Free [A] SOH CAH TOA 8 30° x Example 3 [B] 60° Find missing sides of Right Triangles Calculator Free x 12 SOH CAH TOA 12 sin 60 x 3 12 2 x x 3 24 24 x 3 24 3 x 8 3 3 Example 3 Find missing sides of Right Triangles Calculator Free [C] 45° x 12 SOH CAH TOA Example 3 Find missing sides of Right Triangles Calculator Free [D] 45° 10 x SOH CAH TOA x sin 45 10 2 x 2 10 2 x 10 2 x 5 2 Example 4 Solve a Triangle Solve triangle ABC. Round lengths to the nearest tenth. C 10 Angles A= B= C= 35° A B Sides a= b= c= Example 5 Solve a Triangle with Missing Angle Solve triangle ABC. Round lengths to the nearest tenth. C 5 A 12 B Angles A= B= C= Sides a= b= c= Example 6 Angle of Elevation and Depression Line of Sight Angle of Depression Angle of Elevation Line of Sight