The unit circle

12 questions

1. In a right triangle, if the hypotenuse is 37.5 cm and a second side is 30 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. An isosceles triangle has an internal angle of 50ᵒ, what might the other two angles be?
4. In a right triangle, if the shortest sides are 36 cm and 48 cm, what is the length of the hypotenuse? (Use a calculator to help you.)
5. Would a triangle ABC with sides AB = 10cm, BC = 7.5cm, AC = 12.5cm 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. What is the value of θ for sin(θ) = 1?
8. What is the value of θ for tan(θ) = 1?
9. What is the value of θ for cos(θ) = 0?
10. What is the value of θ for sin(θ) = cos(θ)?
11. What is the value of θ for sin(θ) = tan(θ)?
12. What is cos(60ᵒ)?

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