Starter quiz
- In a right triangle, if the hypotenuse is 75 cm and a second side is 60 cm, what is the length of the third side? (Use a calculator to help you.)
- 50 cm
- 45 cm ✓
- 54 cm
-
- Which of the following statements is true for these triangles?
- The triangles are similar.
- The triangles are not similar. ✓
- It is not possible to know whether the triangles are similar or not.
-
- In a right triangle, if the shortest sides are 7.5 cm and 18 cm, what is the length of the hypotenuse? (Use a calculator to help you.)
- 19.5 cm ✓
- 18.5 cm
- 20.5 cm
-
- Would a triangle ABC with sides AB = 16cm, BC = 10cm, AC = 21cm be similar to the one shown in the diagram?
- Yes
- No ✓
-
- Would a triangle ABC with sides AB = 12 cm, BC = 9 cm, AC = 15 cm be similar to the one shown in the diagram?
- Yes ✓
- No
-
- For this pair of triangles, can you determine whether they are similar without using side lengths?
- Yes, because their three angles correspond. ✓
- No because you only know two angles.
- No, because you always need a side and two angles.
-
Exit quiz
- Using triangle ABC, if θ = 38ᵒ and hypotenuse AB = 14 cm, what is the length of the adjacent side AC to 1 d.p. ?
- '11.0' ✓
- What is the value of cos(20ᵒ) to 2 d.p. ?
- 0.93
- 0.94 ✓
- 0.92
-
- Using triangle ABC, if θ = 38ᵒ and AC = 6 cm, what is the length of the hypotenuse AB to 1 d.p. ?
- '7.6' ✓
- What does the 'co' in Cosine mean?
- Complementary ✓
- Coordinate
- Core
- Conditional
-
- Using triangle ABC, if θ = 30ᵒ and AC = 12 cm, what is the length of the hypotenuse AB to 1 d.p. ?
- '13.9' ✓
- Using triangle ABC, if θ = 30ᵒ and AC = 9 cm, what is the length of the hypotenuse AB to 1 d.p. ?
- '10.4' ✓
Worksheet
Presentation
Lesson Details
Key learning points
- The cosine ratio involves the hypotenuse, adjacent and the angle.
- If you know the length of the hypotenuse and the size of the angle, you can use the cosine ratio.
- If you know the length of the adjacent and the size of the angle, you can use the cosine ratio.
- If you know the length of the hypotenuse and adjacent, you can use the cosine ratio.
Common misconception
The cosine formula is only used to find the length of a side adjacent to an angle.
The cosine formula can be used to find the length of a side adjacent to an angle. A rearrangement of the formula also allows us to find the length of the hypotenuse given the adjacent side. The arccosine 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.
Adjacent - The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.