Geometry Chapter 8 Test



Day 08 Geometry Part 2 Unit Test Review Name__________________________

SHOW ALL WORK BELOW EACH PROBLEM. Date_________________Block______

Right Triangles

Target 1: Are these the sides of a right triangle, obtuse triangle, or acute triangle? Show your work!

If it is a right triangle, tell whether or not it is a Pythagorean Triple. (yes or no?)

1. 12, 16, and 20 _____________________ _________

2. 4, 5, and 6 _____________________ _________

3. 1, [pic], and 2[pic] _____________________ _________

4. 5, 10, and 12 _____________________ _________

Target 1-2: Using Pythagorean Theorem, find each side length rounded to the nearest tenth.

5. x = _______ 6. x = _______ 7. x = _______

Target 2: Using special Right Triangle Formulas (30(-60(-90( or 45(-45(-90(), find each side length expressed in simplified radical form OR in decimal form rounded to the tenth.

8. x = _____ y = _____ 9. x = _____ y = _____ 10. x = _____ y = _____

11. x = _____ y = _____ 12. x = _____ y = _____ 13. x = _____ y = _____

Target 4: Write each trigonometric ratio as a fraction in simplest form.

14. sin X = _________ 15. cos X = _________ 16. tan X = _________

17. sin Y = _________ 18. cos Y = _________ 19. tan Y = _________

20. What is m(X? _________ 21. What is m(Y? _________

Target 3: Use Trigonometry to find the value of x. Write an equation for each problem.

Round sides to the nearest tenth and angles to the nearest degree.

22. x = _________ 23. x = _________ 24. x = _________

25. x = _________ 26. x = _________ 27. x = _________

28. x = _________ 29. x = _________ 30. x = _________

Target 3: Solve each word problem. Complete each picture, show your work, and round all answers to the nearest integer.

31. Jacob went to the Norfolk Zoo. The angle of depression from the 18 foot giraffe to Jacob was 44(.

How far away from the giraffe’s feet was Jacob?

_____________

32. A captain of a ship spots the top of a lighthouse at a 35( angle of elevation. He knows that the

lighthouse is 80 feet above the shore line. How far is the ship from lighthouse?

_____________

33. A coconut fell from a 15 foot palm tree and rolled about 13 feet away from it. Find the angle of

elevation from the coconut to top of the palm tree.

_____________

34. A woman standing on a cliff at the edge of the ocean spots a raft. The cliff is 19 meters above sea level

and the angle of depression to the ocean is 5(. Find the distance from the raft to the base of the cliff.

_____________

Know the following terms, what they mean, and how to use them in solving problems.

Draw a picture and write out the formulas for those that apply for each term.

← Angle of Elevation

← Angle of Depression

← Pythagorean Theorem

← Pythagorean Triple

← Test for Right Triangle

← Test for an Acute Triangle

← Test for an Obtuse Triangle

← 30(-60(-90( Special Right Triangle Formula

← 45(-45(-90( Special Right Triangle Formula

← Trigonometric Ratio

← Sine

← Cosine

← Tangent

-----------------------

x

[pic]

10

[pic]11

x

x

5

8

x

y

30(

[pic]

x

y

[pic]5

60(

45(

14

y

x

12

y

x

60(

45(

x

y

[pic]

4. 4

x

y

4

3

4

5

10

X

Z

Y

50ft

x

12(

x

38

47(

120

40

x(

400 ft.

x

45(

13

7

x(

x

14.5

51(

130 ft.

25(

x

2,000 ft.

9,000 ft

x(

12,000 ft

x

49(

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