Finding Trigonometric Ratios
FINDING TRIGONOMETRIC RATIOS +
FINDING MISSING SIDES OF RIGHT TRIANGLES Summit Public School
THE PYTHAGOREAN THEOREM In this formula, it is important to note that c is always the hypotenuse, which is the longest side of the right triangle and is located across from the right angle.
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TRIGONOMETRY When dealing with right triangles, there are three important ratios we look atβ¦
3
THE TRIGONOMETRIC RATIOS!
SOH
CAH
TOA
opposite
adjacent
opposite
hypotenuse
hypotenuse
adjacent
4
THE TRIG RATIOS ARE DIFFERENT FOR EACH OF THE ACUTE ANGLES IN A RIGHT TRIANGLE!!!
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PRACTICE 1 ο Complete the table for the diagram: Angle π½ sin π½ =
cos π½ =
tan π½ =
6
PRACTICE 2 ο Complete the table for the diagram: Angle πΆ sin πΆ =
cos πΆ =
tan πΆ =
7
PRACTICE 3 ο In βπππ, it is known that πβ π = 90Β°. Complete the table below. Angle M
Angle N
sin π =
sin π =
cos π =
cos π =
tan π =
tan π = 8
PRACTICE 4 ο Complete the table for the diagram: Angle L
Angle N
sin πΏ =
sin π =
cos πΏ =
cos π =
tan πΏ =
tan π =
9
PRACTICE 5 Use the diagram to complete the table.
ANGLE
sin(angle) = opp/hyp (SOH)
cos(angle) = adj/hyp (CAH)
tan(angle) = opp/adj (TOA)
A
sin (A) =
cos (A) =
tan (A) =
C
sin (C) =
cos (C) =
tan (C) = 10
PRACTICE 6 ο Complete the table for the diagram: Angle π½
9
sin π½ = 40 cos π½ =
tan π½ =
11
PRACTICE 7 ο Complete the table for the diagram: Angle π½
1
sin π½ = 7 cos π½ =
tan π½ =
12
PRACTICE 8
π π¬π’π§ π = ππ
ο In a right triangle, suppose you know the trigonometric ratio above. ο Evaluate the following. It may help to draw a right triangle (x is any acute angle)!
ππ¨π¬ π = πππ§ π = 13
PRACTICE 9
π πππ§ π = π
ο In a right triangle, suppose you know the trigonometric ratio above. ο Evaluate the following. It may help to draw a right triangle (x is any acute angle)!
ππ¨π¬ π = π¬π’π§ π = 14
PRACTICE 10
5 2 ππ. 5 ππ.
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PRACTICE 11 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 12 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 13 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 14 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 15 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 16 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 17 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 18
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PRACTICE 19
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PRACTICE 20
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PRACTICE 21 ο A ladder is leaning against a wall. It is known that the top of the ladder is 4 feet from the floor and the bottom of the ladder forms a 9Β° angle of elevation with the floor. How long is the ladder?
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PRACTICE 22 ο A ladder is leaning against a wall. Suppose you are standing 6 feet away from the wall at the bottom of the ladder, and the bottom of the ladder forms a 20Β° angle of elevation with the floor. How long is the ladder?
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PRACTICE 23
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FINDING MISSING SIDES OF RIGHT TRIANGLES Summit Public School
THE PYTHAGOREAN THEOREM In this formula, it is important to note that c is always the hypotenuse, which is the longest side of the right triangle and is located across from the right angle.
2
TRIGONOMETRY When dealing with right triangles, there are three important ratios we look atβ¦
3
THE TRIGONOMETRIC RATIOS!
SOH
CAH
TOA
opposite
adjacent
opposite
hypotenuse
hypotenuse
adjacent
4
THE TRIG RATIOS ARE DIFFERENT FOR EACH OF THE ACUTE ANGLES IN A RIGHT TRIANGLE!!!
5
PRACTICE 1 ο Complete the table for the diagram: Angle π½ sin π½ =
cos π½ =
tan π½ =
6
PRACTICE 2 ο Complete the table for the diagram: Angle πΆ sin πΆ =
cos πΆ =
tan πΆ =
7
PRACTICE 3 ο In βπππ, it is known that πβ π = 90Β°. Complete the table below. Angle M
Angle N
sin π =
sin π =
cos π =
cos π =
tan π =
tan π = 8
PRACTICE 4 ο Complete the table for the diagram: Angle L
Angle N
sin πΏ =
sin π =
cos πΏ =
cos π =
tan πΏ =
tan π =
9
PRACTICE 5 Use the diagram to complete the table.
ANGLE
sin(angle) = opp/hyp (SOH)
cos(angle) = adj/hyp (CAH)
tan(angle) = opp/adj (TOA)
A
sin (A) =
cos (A) =
tan (A) =
C
sin (C) =
cos (C) =
tan (C) = 10
PRACTICE 6 ο Complete the table for the diagram: Angle π½
9
sin π½ = 40 cos π½ =
tan π½ =
11
PRACTICE 7 ο Complete the table for the diagram: Angle π½
1
sin π½ = 7 cos π½ =
tan π½ =
12
PRACTICE 8
π π¬π’π§ π = ππ
ο In a right triangle, suppose you know the trigonometric ratio above. ο Evaluate the following. It may help to draw a right triangle (x is any acute angle)!
ππ¨π¬ π = πππ§ π = 13
PRACTICE 9
π πππ§ π = π
ο In a right triangle, suppose you know the trigonometric ratio above. ο Evaluate the following. It may help to draw a right triangle (x is any acute angle)!
ππ¨π¬ π = π¬π’π§ π = 14
PRACTICE 10
5 2 ππ. 5 ππ.
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PRACTICE 11 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 12 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 13 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 14 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 15 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 16 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 17 ο Find the values of the missing side lengths in the triangle below.
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PRACTICE 18
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PRACTICE 19
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PRACTICE 20
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PRACTICE 21 ο A ladder is leaning against a wall. It is known that the top of the ladder is 4 feet from the floor and the bottom of the ladder forms a 9Β° angle of elevation with the floor. How long is the ladder?
26
PRACTICE 22 ο A ladder is leaning against a wall. Suppose you are standing 6 feet away from the wall at the bottom of the ladder, and the bottom of the ladder forms a 20Β° angle of elevation with the floor. How long is the ladder?
27
PRACTICE 23
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