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Setting up trig ratios and solving right triangles.
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I can label the sides of a right triangle.I can set up the trig ratios.
I can use the trig ratios to solve for the missing side length & angle measures of a
right triangle.
Solving Right TrianglesDay 2
H
AT
15
9
Calculate the length of
hypotenuse
leg
leg
?
Use the Pythagorean theorem
-81 -81
x = 12
H
AT
15
9
hypotenuse
Opp. leg
Adj. leg
12
Set up the following trig ratios
Sin H =
Cos H =
Tan H =
Sin A =
Cos A =
Tan A =
Adj. leg
Opp. leg
HS
C
Calculate the length of
hypotenuse
legleg
?
Use the Pythagorean theorem
x = 6
hypotenuse
Set up the following trig ratiosAd
j. le
g
Opp. leg
HS
C
6
Sin S =
Cos S =
Tan S =
Sin H =
Cos H =
Tan H =
Adj.leg
Opp.leg
If Sin A = , find the Cos A.
*Draw a triangle and label.
hypotenuse
A
Opp. le
g
Adj. leg
68
x-36 -36
Cos A =
Use the last example as a model problem to complete the following:
1. If Tan A = , find Sin B.
2. If Cos B = , find Tan A.
Solving Right Triangles means to calculate missing side lengths and angle measures of
a right triangle.
When evaluating sine, cosine, or tangent you need to make sure your calculator is in degree mode.
MODE Radian Degree
Evaluating Angles in the calculator.
(A) Sin 52o
(B) Cos 122o
(C) Tan 45o
(D) Sin 0o
(E) Cos 90o
(F) Tan 90o
A
B
C
x y
250
37o
Solve for x and y
Why can’t you use the Pythagorean Theorem?
hypotenuseOpp. leg
Adj. leg
Which side should be the longest? Why?
Solve for x and y
A
B
Cx
y 10
61o
hypo
tenu
seOpp. leg
Adj. leg
Solve for x and y
A
B
C
x
y 13
34
o
hypo
tenu
seOpp. leg
Adj. leg
Using the inverse function to solve for angles
Notice if you use the 2nd button and then choose a trig function, you are using the inverse.
Sin-1 Cos-1
Tan-1
(a) (b)Sin-1 Sin-1 Cos-1 Cos-1
Use the examples on the previous slide as model problems to help complete the following problems.
(c) (d)
(e) (f)
Sin-1Sin-1
Find the measures of the acute angles in a right triangle.
*Remember: the 2 acute angles of a right triangle are complementary
FIND: m<A and m<B
A
B
C
65.8 11.2
hypotenuse
Opp. leg
Adj. leg
9.8 + 80.2 = 90
A
BC 10.8
24.7
Find the m<A and m<B
A
BC
72
Find the m<A and m<B
