Starter quiz
- In a right triangle, if the hypotenuse is 15 cm and a second side is 9 cm, what is the perimeter? (Use a calculator to help you.)
- 36 cm ✓
- 32 cm
- 41 cm
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- What is the value of θ for cos(θ) = 0
- 90ᵒ ✓
- 45ᵒ
- 30ᵒ
- 0ᵒ
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- In a right triangle, if the hypotenuse is 25 cm and a second side is 15 cm, what is the area? (Use a calculator to help you.)
- ✓
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-
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- Which of these is a rearrangement of
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-
- ✓
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- In a right triangle, if you are provided with θ and the hypotenuse, which function would you use to find the opposite side?
- Sine ✓
- Cosine
- Tangent
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- In a right triangle, if θ = 35ᵒ and the opposite side is 7 cm, what is the length of the hypotenuse to the nearest whole number?
- 12 cm ✓
- 9 cm
- 10cm
-
Exit quiz
- Using triangle ABC, if θ = 35ᵒ and BC = 5 cm, what is the length of the hypotenuse AB to 1 d.p. ?
- '8.7' ✓
- What value of will produce the same result for cos() and sin(30ᵒ)?
- 30ᵒ
- 60ᵒ ✓
- 90ᵒ
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- Using triangle ABC, if θ = 40ᵒ and BC = 4.8 cm, what is the length of the hypotenuse AB to 1 d.p. ?
- '7.5' ✓
- What value of will produce the same result for sin() and cos(26ᵒ)?
- 36ᵒ
- 46ᵒ
- 64ᵒ ✓
- 54ᵒ
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- Using triangle ABC, if θ = 50ᵒ and AB = 12 cm, what is the length of side BC to 1 d.p. ?
- '9.2' ✓
- Using triangle ABC, if θ = 45ᵒ and AB = 18 cm, what is the length of side BC to 1 d.p. ?
- '12.7' ✓
Worksheet
Presentation
Lesson Details
Key learning points
- The sine ratio involves the hypotenuse, opposite and the angle.
- If you know the length of the hypotenuse and the size of the angle, you can use the sine ratio.
- If you know the length of the opposite and the size of the angle, you can use the sine ratio.
- If you know the length of the hypotenuse and opposite, you can use the sine ratio.
Common misconception
The sine formula is only used to find the length of a side opposite an angle.
Whilst the sine formula can be used to find the length of a side opposite an angle, a rearrangement of the formula also allows us to find the length of the hypotenuse given the opposite side. The arcsine function allows us to find the angle, itself.
Keywords
Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
Opposite - The opposite side of a right-angled triangle is the side which is opposite the marked angle.
Trigonometric function - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.