10 Chapter Test

Do you know HOW?

Use the triangle below. Find the missing side length. If necessary, round to the nearest tenth.

1. a = 28 , b = 35 eh equals 28 comma b equals 35
2. a = 12 , b = 35 eh equals 12 comma b equals 35
3. b = 4.0 , c = 4.1 b equals 4.0 comma c equals 4.1

4. a = 10 , c = 26 eh equals 10 comma c equals 26

   

State whether segments of the given lengths can be sides of a right triangle.

5. 7, 24, 25
6. 0.9, 1.2, 1.5
7. 8, 16, 17

Simplify each radical expression.

8. 3 + 12 square root of 3 plus square root of 12
9. 300 square root of 300
10. 4 10 − 10 4 square root of 10 minus square root of 10
11. − 18 12 fraction negative square root of 18 , over square root of 12 end fraction
12. 1 3 + 4 fraction 1 , over square root of 3 plus 4 end fraction
13. 6 4 − 6 fraction square root of 6 , over 4 minus square root of 6 end fraction
14. 2 2 + 3 fraction square root of 2 , over square root of 2 plus 3 end fraction
15. − 3 5 x 3 ⋅ 10 x 3 negative 3 , square root of 5 , x cubed end root , dot . square root of 10 , x cubed end root

Solve the following radical equations. Check your solutions.

16. 2 x + 4 = 7 square root of 2 x end root , plus 4 equals 7
17. k − 8 = 28 square root of k minus 8 equals 28
18. 3 m + 2 3 = 1 fraction square root of 3 m plus 2 end root , over 3 end fraction . equals 1
19. 2 x + 4 = 3 x square root of 2 x plus 4 end root . equals , square root of 3 x end root
20. 2 − x = x square root of 2 minus x end root , equals x
21. − 5 a + 6 = − a square root of negative 5 eh plus 6 end root . equals negative eh

Graph each function.

22. y = x + 2 y equals , square root of x plus 2 end root
23. y = x − 3 y equals , square root of x minus 3 end root
24. y = x + 5 y equals square root of x plus 5

For each triangle, find the missing side length.

25. 
26. 
27. A right triangle has a 50 ° 50 degrees  angle. The hypotenuse is 10 cm long. To the nearest tenth, what is the length of the side opposite the 50 ° 50 degrees  angle?

Do you UNDERSTAND?

28. Reasoning Draw right Δ A B C cap delta eh b c  with ∠ B angle b  as the right angle. What is the relationship between sin A and cos C? Explain.
29. Open-Ended Give an example of a radical equation for which all solutions are extraneous. What is the solution to the equation? How do you know?
30. Reasoning Is the following conditional statement always true? “If a right triangle has a leg that is 3 in. long and a leg that is 4 in. long, then the hypotenuse is 5 in. long.” Is its converse always true? Explain.
31. Writing Explain how you would simplify the radical expression 2 5 + 2 . fraction 2 , over square root of 5 plus 2 end fraction . .
32. Geometry Find the length of a diagonal of a square with a side length of 3 in. Is the length of the diagonal a rational number? Explain.

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