Ratios and Equations
This trigonometry ratio is used when you know the hypotenuse and adjacent sides of a right triangle.
What is cosine?
Find the missing leg.
Leg=x
Leg=4
Hypotenuse=5
What is x=3?
Find the missing side length using sine, cosine, or tangent. Round your answer to the nearest hundredth.
Angle=30 degrees
Opposite=x
Hypotenuse=25
What is x=12.5?
Find the missing angle using inverse sine, inverse cosine, or inverse tangent. Round your answer to the nearest whole degree.
Opposite=12
Hypotenuse= 13
Angle= x
What is x=67 degrees?
A triangle has side lengths 8 cm, 15 cm, and 17 cm.
Use the converse of the Pythagorean Theorem to determine whether the triangle is a right triangle.
What is "the triangle IS a right triangle"?
This trigonometry ratio is used when you know the opposite and hypotenuse sides of a right triangle.
What is sine?
Find the missing hypotenuse.
Leg=16
Leg=30
Hypotenuse=x
What is x=34?
Find the missing side length using sine, cosine, or tangent. Round your answer to the nearest hundredth.
Angle=70 degrees
Adjacent=y
Hypotenuse=9
What is y=3.08?
Find the missing angle using inverse sine, inverse cosine, or inverse tangent. Round your answer to the nearest whole degree.
Adjacent= 1
Hypotenuse= 2
Angle= y
What is y=60?
A pilot flying above the ocean looks down at a ship. This angle from the horizontal is called this.
What is the angle of depression?
This trigonometry ratio is used when you know the opposite and adjacent sides of a right triangle.
What is tangent?
Find the missing hypotenuse. Round your answer to the nearest tenth.
Leg=5
Leg=4
Hypotenuse=x
What is x=6.4?
Find the missing side length using sine, cosine, or tangent. Round your answer to the nearest hundredth.
Angle=20 degrees
Opposite=z
Adjacent=24
What is z=8.74?
Find the missing angle using inverse sine, inverse cosine, or inverse tangent. Round your answer to the nearest whole degree.
Opposite= 0.707
Adjacent= 0.866
Angle= z
What is z=39 degrees?
A person standing on the ground looks at the top of a tall building. This is the name of the angle they are measuring.
What is the angle of elevation?
This equation is used when you know two sides and are looking for a third side in a right triangle.
What is Pythagorean Theorem?
Find the missing leg.
Leg=x
Leg=40
Hypotenuse=41
What is x=9?
Find the missing side length using sine, cosine, or tangent. Round your answer to the nearest hundredth.
Angle= 45 degrees
Opposite= 13
Hypotenuse= x
What is x=18.38?
Find the missing angle using inverse sine, inverse cosine, or inverse tangent. Round your answer to the nearest whole degree.
Angle= x
Hypotenuse= 13
Opposite= 5
What is x=23 degrees?
In a 30-60-90 triangle, the short side is 7. Find the long side.
What is 14?
These equations are used when you know the ratio of sides in a right triangle and want to find the angle.
What are inverse trigonometric ratios ?
Find the missing leg.
Leg=x
Leg=20
Hypotenuse=29
What is x=21?
Find the missing side length using sine, cosine, or tangent. Round your answer to the nearest hundredth.
Angle= 56 degrees
Adjacent= 18
Hypotenuse= y
What is y=32.19?
Find the missing angle using inverse sine, inverse cosine, or inverse tangent. Round your answer to the nearest whole degree.
Angle= y
Adjacent= 5
Opposite= 12
What is y= 67?
In a 45-45-90 triangle, the length of one leg is 9. Find the lengths of the other leg and the hypotenuse.
What is 9 and 9 square root of 2 ?