Starter quiz
- In a right triangle, if the hypotenuse is 32.5 cm and a second side is 12.5 cm, what is the perimeter? (Use a calculator to help you.)
- 75 cm ✓
- 80 cm
- 70 cm
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- What is the value of θ for sin(θ) = tan(θ) ?
- 0ᵒ ✓
- 45ᵒ
- 90ᵒ
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- What is the value of θ for tan(θ) = 1
- 45ᵒ ✓
- 90ᵒ
- 30ᵒ
- 0ᵒ
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- In a right triangle, if the hypotenuse is 32.5 cm and a second side is 12.5 cm, what is the area? (Use a calculator to help you.)
- ✓
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-
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- What is the value of θ for sin(θ) = 1
- 90ᵒ ✓
- 45ᵒ
- 50ᵒ
- 30ᵒ
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- What is the value of θ for sin(θ) = cos(θ) ?
- 45ᵒ ✓
- 90ᵒ
- 30ᵒ
- 0ᵒ
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Exit quiz
- Match the estimated values with the trigonometric functions below.
- sin(23°)⇔0.39 ✓
- cos(39°)⇔0.777 ✓
- tan(22°)⇔0.404 ✓
- tan(45°)⇔1 ✓
- For which value of θ is tan (θ) undefined?
- '90' ✓
- In a right triangle, if you are provided with θ and the opposite side, which function would you use to find the adjacent side?
- Sine
- Cosine
- Tangent ✓
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- Which of these is a rearrangement of
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-
- ✓
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- Which of these is not an rearrangement of
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-
- ✓
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- For a right triangle ABC, if angle CBA = 33ᵒ, and the adjacent side to that angle is 1 cm, what is the length of the side opposite angle CBA?
- 0.545 cm (3 d.p)
- 0.649 cm (3 d.p) ✓
- 1 cm
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Worksheet
Presentation
Video
Lesson Details
Key learning points
- When the adjacent has a length of one, the opposite side has a length of tan(θ).
- You can apply a scale factor to this triangle to find the scaled length of the opposite side.
- There is a multiplicative link between two similar right-angled triangles.
- There is a multiplicative link within each right-angled triangle.
Common misconception
tan(60°) is double tan(30°).
The values of tan of an angle do not scale linearly. From the unit circle, we see that an angle of 30° meets a tangent to the circle at a height of approx. 0.58 units, whilst an angle of 60° meets the same tangent at a height of approx. 1.73 units.
Keywords
Adjacent - The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
Opposite - The opposite side of a right-angled triangle is the side which is opposite the marked angle.
Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.