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opposite adjacent Study of ∆s and relationships between their angles and sides Angles are labeled with uppercase (ex. A) sides are lowercase (ex. a) An angle and its opposite side use the same letter (ex. A and a)
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RIGHT TRIANGLESSine, Cosine, Tangent
8.7 Sine, Cosine, And Tangent
Essential Question: How do you find the side lengths of a triangle that is not special?
opposite adjacentStudy of ∆s and relationships between
their angles and sides
• Angles are labeled with uppercase (ex. A)• sides are lowercase (ex. a)
• An angle and its opposite side use the same letter (ex. A and a)
OH
AOHA
SOH CAHTOA Sine=
Cosine=Tangent=
OH
AH
OA
When finding sin, cos, tan…1. Solve for missing sides2. Mark angle you are using3. Label opp. (O), adj. (A), hyp. (H)4. Write sin, cos, tan ratios5. Rationalize/simplify
OHA 13
222 cba 222 125 c
13c
HOAsin
HAAcos
AOAtan
1312
12135
5
O
H A10√2
222 cba 222 155 b
200c
HOB sin
HAB cos
AOB tan
1510√2
10√2
155
5210c
322
31
22
12
6√3O
H
AHO
30sin
HA
30cos
AO
30tan
126
21
1236
23
366
31
33
Technology Break5min
8.8 Trig Ratios with a Calculator
Essential Question: How do you find side lengths of a triangle that is not special?
= 0.9781= 0.5= 0.2679
When solving for missing sides…1.Mark angle you are working
with2.Label O, A, and H3.SOH? CAH? Or TOA?4.Set-up and solve for missing
side.O
H
ATo find a:CAHTo find b:SOH3022 a
cos
a)(cos2230a827.
3022 bsin
b)(sin2230b211.
SOH CAHTOA
OH
A
To find c:CAHTo find d:TOA
c942cos
429
cosc
112.c
942 dtan
d)(sin429
d18.
Plicker Exit SlipQuestion 1:What is sin(A)?
A)
B)
C)
D)
Question 2:What is tan(25)?
Round to the hundredths.
A) 0.42B) 0.46C) 0.47D) 0.91
√17
2√25
Homework 8.7 ALL 8.8 ALL
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