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....
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Transcript of 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....
![Page 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/1.jpg)
Warm-up #3Warm-up #3
1. Sin 231. Sin 23oo = =2. Cos 782. Cos 78oo = =3. Tan 423. Tan 42oo = =4. Sin A =4. Sin A =5. Sin B =5. Sin B =6. Cos A =6. Cos A =7. Cos B =7. Cos B =8. Tan A =8. Tan A =9. Tan B =9. Tan B =
1312
5 B
A
![Page 2: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/2.jpg)
Solving Right TrianglesSolving Right Triangles
![Page 3: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/3.jpg)
9.6 Solving Rt 9.6 Solving Rt ΔΔss
Essential Question – How do Essential Question – How do we solve right triangles and we solve right triangles and
their applications?their applications?
![Page 4: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/4.jpg)
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 mA= sin-1xIf cos A=x, then mA=cos-1xIf tan A=x, then mA=tan-1x
![Page 5: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/5.jpg)
Pull out your calculatorsPull out your calculatorsFor 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, These are also known as arc sin, arc cos, & arc tan. & arc tan.
![Page 6: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/6.jpg)
Ex: Find the measure of the .sin A=.5
mA=sin-1.5
mA=30o
cos A=.7071
mA=cos-1.7071
mA=45o
tan B=.1051
mB=tan-1.1051
mB=6o
![Page 7: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/7.jpg)
ExampleSolve the Δ
A
BC
__
__
7
24
25
96.25
24sin A mA=sin-1.96 mA=74o
28.25
7sin B
mB=sin-1.28
mB=16o
![Page 8: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/8.jpg)
Ex:solve the Δ (round to the nearest tenth)
____
A B
C
8 10
b
82+102=b2
64+100=b2
164=b2
12.8=b
25.18
10tan A
mA= tan-11.25
mA=51.3o
mB=180-90-51.3=38.7o
![Page 9: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/9.jpg)
Example
S
RT
__
__
r
s
15
20o
1520 sin
r
153420.
r
r=5.1
1520cos
s
159397.
s
1.14s
mS=180-90-20
mS=70o
![Page 10: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/10.jpg)
Examplesolve for x
15.7mi
59mi
x ____
59
7.15tan x
tan x=.2661
x= tan-1.2661
x=14.9o
![Page 11: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/11.jpg)
Assignment
Guided Practice WS
![Page 12: 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.](https://reader034.fdocument.pub/reader034/viewer/2022050920/5513f5225503463a298b620b/html5/thumbnails/12.jpg)
Assessment
Answer the essential question – How do we solve right How do we solve right triangles and their applications?triangles and their applications?