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

Solving Right Triangles

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

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-1x If cos A=x, then mA=cos-1x If tan A=x, then mA=tan-1x

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

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

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

Ex:solve the Δ (round to the nearest tenth) C 82+102=b2 __ __ 10 64+100=b2 8 164=b2 B A 12.8=b b mA=51.3o mA= tan-11.25 mB=180-90-51.3=38.7o

Example S 15 r=5.1 r __ __ 20o T R s mS=180-90-20 mS=70o

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

Assignment Guided Practice WS

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