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Warm-up #3 1. Sin 23 o = 2. Cos 78 o = 3. Tan 42 o = 4. Sin A = 5. Sin B = 6. Cos A = 7. Cos B = 8. Tan A = 9. Tan B = 13 12 5 B A.

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Presentation on theme: "Warm-up #3 1. Sin 23 o = 2. Cos 78 o = 3. Tan 42 o = 4. Sin A = 5. Sin B = 6. Cos A = 7. Cos B = 8. Tan A = 9. Tan B = 13 12 5 B A."— Presentation transcript:

1 Warm-up #3 1. Sin 23 o = 2. Cos 78 o = 3. Tan 42 o = 4. Sin A = 5. Sin B = 6. Cos A = 7. Cos B = 8. Tan A = 9. Tan B = 13 12 5 B A

2 Solving Right Triangles

3 9.6 Solving Rt Δs Essential Question – How do we solve right triangles and their applications?

4 Solving a right Δ To solve a rt Δ: find the measure of all its missing parts (should be 3 sides and 3 s). To find an measure: If sin A=x, then m A= sin -1 x If cos A=x, then m A=cos -1 x If tan A=x, then m A=tan -1 x

5 Pull out your calculators For inverse sine (sin -1 ) press 2 nd sin For inverse cosine (cos -1 ) press 2 nd cos For inverse tangent (tan -1 ) press 2 nd tan These are also known as arc sin, arc cos, & arc tan.

6 Ex: Find the measure of the. sin A=.5 m A=sin -1.5 m A=30 o cos A=.7071 m A=cos -1.7071 m A=45 o tan B=.1051 m B=tan -1.1051 m B=6 o

7 Example Solve the Δ A B C __ 7 24 25 m A=sin -1.96m A=74 o m B=sin -1.28 m B=16 o

8 Ex:solve the Δ (round to the nearest tenth) __ A B C 8 10 b 8 2 +10 2 =b 2 64+100=b 2 164=b 2 12.8=b m A= tan -1 1.25 m A=51.3 o m B=180-90-51.3=38.7 o

9 Example S RT __ r s 15 20 o r=5.1 m S=180-90-20 m S=70 o

10 Example solve for x 15.7mi 59mi x __ tan x=.2661 x= tan -1.2661 x=14.9 o

11 Assignment Guided Practice WS

12 Assessment How do we solve right triangles and their applications? Answer the essential question – How do we solve right triangles and their applications?


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