Using the cosine ratio

12 questions

1. 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.)
2. Which of the following statements is true for these triangles?
3. 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.)
4. Would a triangle ABC with sides AB = 16cm, BC = 10cm, AC = 21cm be similar to the one shown in the diagram?
5. Would a triangle ABC with sides AB = 12 cm, BC = 9 cm, AC = 15 cm be similar to the one shown in the diagram?
6. For this pair of triangles, can you determine whether they are similar without using side lengths?
7. Using triangle ABC, if θ = 38ᵒ and hypotenuse AB = 14 cm, what is the length of the adjacent side AC to 1 d.p. ?
8. What is the value of cos(20ᵒ) to 2 d.p. ?
9. Using triangle ABC, if θ = 38ᵒ and AC = 6 cm, what is the length of the hypotenuse AB to 1 d.p. ?
10. What does the 'co' in Cosine mean?
11. Using triangle ABC, if θ = 30ᵒ and AC = 12 cm, what is the length of the hypotenuse AB to 1 d.p. ?
12. Using triangle ABC, if θ = 30ᵒ and AC = 9 cm, what is the length of the hypotenuse AB to 1 d.p. ?

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