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
Solving Right TrianglesSolving Right Triangles
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?
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
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.
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
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
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
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
Examplesolve for x
15.7mi
59mi
x ____
59
7.15tan x
tan x=.2661
x= tan-1.2661
x=14.9o
Assignment
Guided Practice WS
Assessment
Answer the essential question – How do we solve right How do we solve right triangles and their applications?triangles and their applications?
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