Download Deductive versus Inductive Reasoning

Right Triangle Trigonometry
Objectives:
 Calculate the lengths of sides and angles of a right triangle using
trigonometric ratios.
 Solve word problems involving right triangles and trigonometric
ratios.
 Use the two column proof method to prove a geometric result
Vocabulary:
 none
Formulas:
hypotenuse
opposite
adjacent
A
sin(A) 
cos(A ) 
tan(A ) 
Special Triangles:
60
2
2
45
1
30
3
Right Triangle Trigonometry
1
45
1
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Possible Classroom Examples:
Use Trigonometric ratios to find the unknown sides and angles in the right
triangles below:
B
x
45
y
x
5
A
30
y
8
Use Trigonometric ratios to find the unknown sides and angles in the right
triangles below:
a
B
c
A
b
a
B
c
A
b
a
b  6.5 mA  54.3
B
a  6.0 b  7.0
c
b
A
Right Triangle Trigonometry
c  .92 mB  49.9 
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A support cable runs from the top of the telephone pole to a point on the
ground 42.7 feet from its base. If the cable makes an angle of 29.6 with
the ground, find (rounding to the nearest tenth of a foot)
pole
29.6
42.7 ft
a. the height of the pole
b. the length of the cable
You are hiking along a river and see a tall tree on the opposite bank. You
measure the angle of elevation of the top of the tree and find it to be 61.0.
You then walk 50 feet directly away from the tree and measure the angle of
elevation. If the second measurement is 49.5, how tall is the tree? Round
your answer to the nearest foot.
49.5 61.0
tree
50 ft
Right Triangle Trigonometry
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