Name ________________________

Lesson 54 PRACTICE: Special Right Triangles PART 1: Find the value of each variable. If the answer is not an integer, express it in simplest radical form.

1.

2.

3.

x = ____________ y = ____________

x = ____________ y = ____________

x = ____________ y = ____________

4.

5.

6.

x = ____________ y = ____________

x = ____________ y = ____________

x = ____________ y = ____________

7.

8.

9.

x = ____________ y = ____________

x = ____________ y = ____________

x = ____________ y = ____________

10.

11.

12.

x = ____________ y = ____________

x = ____________ y = ____________

x = ____________ y = ____________

13.

14.

15.

x = ____________ y = ____________

x = ____________ y = ____________

x = ____________ y = ____________

16.

17.

18.

a = ____________ b = ____________ c = ____________ d = ____________

a = ____________ b = ____________ c = ____________ d = ____________

a = ____________ b = ____________ c = ____________

19.

20.

21.

a = ____________ b = ____________ c = ____________

a = ____________ b = ____________

a = ____________ b = ____________

22.

23.

24.

x = ____________ y = ____________

x = ____________ y = ____________

x = ____________ y = ____________

PART 2: Find the value of each variable. If the answer is not an integer, express it in simplest radical form.  

25.

26.

27.

x = ____________ y = ____________

x = ____________ y = ____________

GF = ____________ FE = ____________ FD = ____________ DE = ____________

28. Find the length of a diagonal of a square whose perimeter is 48.

29. A diagonal of a square has length 8. What is the perimeter of the square?

30. An altitude of an equilateral triangle has length

€

6 3 . What is the perimeter of the triangle?

31. Find the altitude of an equilateral triangle if each side is 10 units long.

32. Right triangle ABC has area 32 3 square centimeters. The measure of ∠A=30

and m∠B=90. Find the length of the sides.

BC = _______ AB = ________ AC = ________

33. After heavy winds damaged a house, workers placed a 6 meter brace against its side at a 45° angle. Then, at the same spot on the ground, they placed a second, longer brace to make a 30° angle with the side of the house.

a. How long is the longer brace? Round to the nearest tenth of a meter.

b. About how much higher does the longer brace reach

than the shorter brace?

34. Find the length d , in simplest radical form, of the diagonal of a cube with edges of the

given length.

a. 1 unit

b. 2 units

c. s units

Special Right Triangles - ANSWERS

1. 2. 3. x = 9 2 y =9 2

x = 11 y =11

x = 4 y = 8

4. 5. 6.

x = 7 y = 7 3

x = 16 y =8

x = 20 y =20 2

7. 8. 9.

x = 24 y =24

x = 10 y =10 3

x = 7 3 y = 7

10. 11. 12.

x = 18 y = 18 3

x = 15 3 y = 30

x = 8 y =4

         

13.

14. 15.

x = 22 2 y = 22 2

x = 8 2 y =8 2

x = 6 2 y = 12

16. 17. 18.

a = 9 3 b = 9 6 c = 27 d = 9 3

a = 12 b = 12 c = 12 3 d = 24

a = 10 2 b = 20 c = 20 2

19. 20. 21.

a = 18 b = 6 3 c = 12 3

a = 22 b = 19 2

a = 15 b = 30− 5 3

22. 23. 24. x = 10 y = 4 2

x = 3 y = 9

x = 8 2 y = 4 6

 

     

25.

26.

27.

x = 3 3 y = 9

x = 4

y = 4 33

GF = 22 FE = 11 2 FD = 22 2 DE =

€

11 6

28. 12 2

29. 16 2

30. 36

31. 5 3

32. BC = 8 AB = 8 3 AC = 16

33. a. 8.5 m b. 3.1 m

34.

a. 3 b. 2 3 c. s 3