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# Worksheet 9A- part 2 - Henry County Schools - trig calculator mathway

Math 2 Unit 2 Name ______________
Worksheet 2A- part 1
Right Triangle Review/Prep for Trig Unit

The Pythagorean Theorem states:
In a right triangle the sum of the _______________ of the legs is equal to the square of the _______________________. c
That is to say, a2 + b2 = c2 a b

In questions 1-3, use the Pythagorean theorem to solve for the indicated variables.
1. 2. 3.

x = ___________ x = ____________ x = ___________

Special Right Triangle Review

In questions 4-12 , use what we learned about special right triangles to find the value of x and y. Show your work for full credit.

4. 5. 6.

x = __________ x = __________ x = __________

7. 8. 9.

x = __________ x = __________ x = __________

10. 11. 12.

x = __________ x = __________ x = __________

y = __________ y = __________ y = __________
Worksheet 2A- part 2

(If you didn’t finish Worksheet 9A – given out after the Unit 8 Test – make sure you do that now!)

A. Find the 5 HIGHLIGHTED Pythagorean Triples on the notes page, and
write them here (these are known by some as Pythagorean PRIMITIVES.)
Then write 4 more triples that are multiples of the PRIMITIVES – these are
also TRIPLES and are very handy to know / be able to recognize for trig work.

1) 2) 3)

4) 5)

B. We have practiced plenty of simpler examples of PYTHAGOREAN THEOREM and SPECIAL RIGHT TRIANGLES – now apply that work to the following problems:

6. Find the perimeter of the square with the given diagonal.

7. Find the perimeter of the rectangle.

8. Find the altitude of this equilateral triangle.

HINT: What are the measures
of the angles in an
equilateral triangle?

9. Find the missing lengths

10. Find the missing lengths.

Math 2 Unit 2 Lesson 2.6A Trigonometric Ratios
Use the definitions of the three trig ratios to complete each statement.

1. 2.
sin A = ________ w sin C = _______

cos A = ________ y cos C = _______

tan A = ________ tan C = _______

3. 4.

5. 6.
24

Use trig ratios and your calculator to approximate each length to the nearest tenth (these are all RIGHT triangles).

7. 8.

9. 10.

11. 12.

Math 2 Unit 2 Lesson 2.6A Trigonometric Ratios, Angles

Write an equation using the appropriate trig ratio for finding the measure of the given angle(s). Then find the measure(s) to the nearest tenth.

1. 2.
[pic] [pic]

3. 4.

[pic] [pic]

5. 6.

[pic] [pic]

Use trig ratios and your calculator to approximate each length and angle measure to the nearest tenth (these are all RIGHT triangles).

7. 8.

9. 10.

11.

1200’ 1500’

Math 2 Unit 2 Lesson 2.6B Trigonometric Ratios Aplications

For each problem, draw a picture/diagram showing the right triangle. Then write a trig ratio equation, and solve the equation to answer the problem.

*The angle between the HORIZONTAL and a line of sight is called an angle of elevation or an angle of depression (see notes for help).

1. A 20-foot ladder is leaning against a wall. The base of the ladder is 3 feet from the wall. What angle does the ladder make with the ground?

2. How tall is a bridge if a 6-foot tall person standing 100 feet away can see the top of the bridge at an angle of 30 degrees to the horizon?

3. An air force pilot must descend 1500 feet over a distance of 9000 feet to land smoothly on an aircraft carrier. What is the plane’s angle of descent?

4. An eagle spotted a mouse 20 feet below at an angle of 42 degrees with the horizon. If the eagle flies along its line of sight, how far will it have to fly to reach its prey?

5. In a movie theatre 150 feet long, the floor is sloped so there is a difference of 30 feet between the front and back of the theater. What is the angle of depression?

EXTRA CREDIT - @ teacher’s discretion

Make up your own trig word problem and illustrate it (by hand or with computer art), and turn it in on a separate unlined 8 ½ by 11 sheet of paper. Include the correct solution on a separate sheet.

-----------------------
12

15

x

13

x

10

12

x

16

Key
S.L.=short leg
Hyp= hypotenuse
L.L=long leg

Summary:

45-45-90 30-60-90
2 legs are [pic] S.L is your reference leg (always find it FIRST)
Hyp= [pic]LEG L.L=S.L[pic] S.L=[pic] S.L=[pic]
Leg=[pic] HYP=S.L[pic]

28

9[pic]

x

45[pic]

13

x

45[pic]

45[pic]

x

x

45[pic]

24

9

x

x

7[pic]

45[pic]

45[pic]

x

x

18

y

60[pic]

[pic]

x

x

30[pic]

30[pic]

10[pic]

y

y

Name ______________________ Date ____________

14[pic]

15

9

12

k

60[pic]

[pic]

p

m

x

n

14

48

n

d

Name ______________________ Date ____________

C

p

m

x

n

A

A

F

B

15

8

15

C

G

sin B = _______ sin A = ______

cos B = ______ cos A = _____

tan B = ______ tan A = ______

9

E

sin F = _______ sin G = ______

cos F = ______ cos G = _____

tan F = ______ tan G = ______

X

C

Z

A

B

15

Y

sin B = _______ sin A = ______

cos B = ______ cos A = _____

tan B = ______ tan A = ______

sin X = _______ sin Z = ______

cos X = ______ cos Z = _____

tan X = ______ tan Z = ______

20”

65[pic]

17 cm

35[pic]

a

b

48 cm

x

15[pic]

70[pic]

h

36 yds

d

y

128’

36ft

40[pic]

35[pic]

Name ______________________ Date ____________

8

6

12

8

A

C

F

B

4

30

15

9

Z

12

13

G

7

21

x[pic]

y[pic]

17

x[pic]

y[pic]

15

14

48 cm

w

61

z

y[pic]

x[pic]

52 cm

11

y[pic]

x[pic]

Name ______________________ Date ____________

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