Right triangle trigonometry relates the angles and side lengths of right triangles using the three main trigonometric functions: sine, cosine, and tangent
Sine (sin) is defined as Opposite / Hypotenuse.
Match the trigonometric function with its definition:
Sine ↔️ Opposite / Hypotenuse
Cosine ↔️ Adjacent / Hypotenuse
Tangent ↔️ Opposite / Adjacent
In a right triangle with θ = 30°, opposite = 5 cm, and hypotenuse = 10 cm, what is sin(θ)?
0.5
In a right triangle with θ = 30°, opposite = 5 cm, and hypotenuse = 10 cm, cos(θ) is approximately 0.866
What is tan(θ) in a right triangle with θ = 30°, opposite = 5 cm, and adjacent = √(75) cm?
0.577
The hypotenuse is always the longest side in a right triangle.
In a right triangle, the hypotenuse is opposite the right angle
Match the side of a right triangle with its definition:
1️⃣ Hypotenuse: Longest side, opposite the right angle
2️⃣ Opposite: Side across from the reference angle
3️⃣ Adjacent: Side next to the reference angle but not the hypotenuse
What is the definition of sine in right triangle trigonometry?
Opposite / Hypotenuse
In a right triangle with θ = 30°, opposite = 5 cm, and hypotenuse = 10 cm, sin(θ) = 0.5.
In a right triangle with θ = 30°, the value of cos(θ) is approximately 0.866
What is the definition of tangent in right triangle trigonometry?
Opposite / Adjacent
Match the side of a right triangle with its definition:
Hypotenuse ↔️ Longest side, opposite the right angle
Opposite ↔️ Side across from the reference angle
Adjacent ↔️ Side next to the reference angle but not the hypotenuse
The hypotenuse is opposite the reference angle in a right triangle.
False
In a right triangle with θ, opposite = 6 cm, and hypotenuse = 10 cm, the value of sin(θ) is 0.6
What is the approximate value of cos(θ) in a right triangle with opposite = 6 cm, hypotenuse = 10 cm, and adjacent = 8 cm?
0.8
Tangent (tan) is defined as Opposite / Adjacent.
What is the definition of sine in right triangle trigonometry?
Opposite / Hypotenuse
Cosine (cos) is defined as Adjacent / Hypotenuse
In a right triangle, the hypotenuse is the longest side.
What are the three main trigonometric functions used in right triangle trigonometry?
Sine, cosine, tangent
In a right triangle, the longest side opposite the right angle is called the hypotenuse
The hypotenuse is always the longest side in a right triangle.
Which side in a right triangle is across from the reference angle?
Opposite
The side next to the reference angle in a right triangle, but not the hypotenuse, is called the adjacent
Identify the sides of right triangle ABC with reference angle ∠A:
1️⃣ Hypotenuse: AC
2️⃣ Opposite: BC
3️⃣ Adjacent: AB
What is the formula for sine in terms of right triangle sides?
Opposite / Hypotenuse
The formula for cosine in terms of right triangle sides is Adjacent / Hypotenuse
The formula for tangent is Opposite / Adjacent.
In a right triangle, if the opposite side is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm, what is the approximate value of sin(θ)?
0.385
If the opposite side is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm, then tan(θ) ≈ 0.417
In a right triangle, cos(θ) can be calculated as Adjacent / Hypotenuse.
In a right triangle with angle θ, where the opposite side is 5 cm, the adjacent side is 12 cm, and the hypotenuse is13 cm, what is the exact value of cos(θ)?
12 / 13
Match the trigonometric function with its definition:
Sine ↔️ Opposite / Hypotenuse
Cosine ↔️ Adjacent / Hypotenuse
Tangent ↔️ Opposite / Adjacent
To calculate sine, cosine, or tangent, you must identify the opposite, adjacent, and hypotenuse sides correctly.
What is the primary use of sine, cosine, and tangent in right triangles?
Relate angles and side lengths
In a right triangle, if θ = 30° and the hypotenuse is 10 cm, the opposite side (x) can be found using sine
If θ = 30° and the hypotenuse is 10 cm in a right triangle, what is the length of the opposite side?
5 cm
The inverse of tangent is used to find the angle when the opposite and adjacent sides are known.