Download Geometry B

Geometry B
Unit 6
Lesson 0 Practice
Name
Represent each square root in simplified form and approximate form.
1)
2)
3)
4)
54
18
48
30
5)
=
=
=
=
=
≈
≈
≈
≈
≈
81
Simplify the following. Give your answer in exact and approximate form.
6)
7)
8)
9)
1
2
5
2
3
3
8
3
= ___________ ≈ ____________
10)
= ___________ ≈ ____________
11)
= ___________ ≈ ____________
= ___________ ≈ ____________
12)
13)
7
2 2
4 3
2
9 3
2
10 5
2
= ___________ ≈ ____________
= ___________ ≈ ____________
= ___________ ≈ ____________
= ___________ ≈ ____________
Perform the operations. Give your answer in exact and approximate form.
= ___________ ≈ ____________
18) 4 3  3
6 3
2
= ___________ ≈ ____________
19)
16) 5 2  2
= ___________ ≈ ____________
20) 9 5  2
5 3
2
= ___________ ≈ ____________
21)
14) 4  2
15)
17)
= ___________ ≈ ____________
4 3 3

= ___________ ≈ ____________
3
1
4 3
3
= ___________ ≈ ____________
= ___________ ≈ ____________
Geometry B
Unit 6
Lesson 1 Practice
Name
Fill in the missing angle in each triangle.
Also, find the exact values of x and y in the special right triangles and their approximate values (if
necessary) to two decimal places.
Please show some work that shows how you got your answer.
1)
x = ___________ ≈ ____________
y = ___________ ≈ ____________
2)
x = ___________ ≈ ____________
y = ___________ ≈ ____________
3)
x = ___________ ≈ ____________
y = ___________ ≈ ____________
4)
m = ___________ ≈ ____________
n = ___________ ≈ ____________
5)
m = ___________ ≈ ____________
n = ___________ ≈ ____________
6)
a = ___________ ≈ ____________
b = ___________ ≈ ____________
7)
v = ___________ ≈ ____________
u = ___________ ≈ ____________
Geometry B
Unit 6
Lesson 2 Practice
Name
1) Complete the following using triangle ABC at the right.
a) Use a centimeter ruler to measure the side lengths of triangle ABC.
b) From angle A, find the following ratios rounded to four decimal places.
opposite
=
hypotenuse
adjacent
=
hypotenuse
opposite
=
adjacent
c) Use a protractor to measure angle A =
d) Fill in the measure of angle A and use a calculator to find the following rounded to four decimal
places.
sin___ =
cos___ =
tan____ =
e) Are your values in part b close to your answers in part d? (They should be!)
2) Write each trigonometric function as a fraction.
sinC =
cosC =
tan A =
tanC =
cos A =
sin A =
3) Write each trigonometric function as a fraction.
cosD =
cosF =
tanD =
sinF =
tanF =
sinD =
4) In question #3, you should notice that cos D  sin F and sin D  cos F . In question #2, you should
also notice that sinC  cos A and cosC  sin A . Will this happen for any right triangle? Explain
why.
5) Find the approximate value of each of the following without typing them in a calculator, rounding
to four decimal places.
a) sin 42 = ____________
b) cos10 = ____________
c) tan 45 = ____________
6) Use your calculator to find values of sine, cosine, and tangent for the following angles. Round to 4
decimal places.
sin 0° = __________
sin 1° = __________
sin 5° = __________
sin 20° = __________
sin 30° = __________
sin 40° = __________
sin 45° = __________
sin 50° = __________
sin 60° = __________
sin 70° = __________
sin 80° = __________
sin 85° = __________
sin 89° = __________
sin 89.9° = __________
sin 89.99° = __________
cos 0° = __________
cos 1° = __________
cos 5° = __________
cos 20° = __________
cos 30° = __________
cos 40° = __________
cos 45° = __________
cos 50° = __________
cos 60° = __________
cos 70° = __________
cos 80° = __________
cos 85° = __________
cos 89° = __________
cos 89.9° = __________
cos 89.99° = __________
tan 0° = __________ (explained later)
tan 1° = __________
tan 5° = __________
tan 20° = __________
tan 30° = __________
tan 40° = __________
tan 45° = __________
tan 50° = __________
tan 60° = __________
tan 70° = __________
tan 80° = __________
tan 85° = __________
tan 89° = __________
tan 89.9° = __________
tan 89.99° = __________
Conclusions
▪ As an angle increases from 0° to 90°, the sine value __________________________.
▪ As an angle increases from 0° to 90°, the cosine value __________________________.
▪ As an angle increases from 0° to 90°, the tangent value __________________________.
▪ For what degree angle between 0° and 90°, does the sine value equal the cosine value? _______Why?
▪ The sine of angle between 0° and 90° is always between ________ and _________.
▪ The cosine of angle between 0° and 90° is always between ________ and _________.
▪ The tangent of angle between 0° and 90° is always between ________ and _________.
45o
30o
1
45o
60o
1
1
7) Fill in the missing sides of the special right triangles, and use them to find the exact value of the
following.
sin 45
sin 30
sin 60
cos 45
cos 30
cos 60
tan 45
tan 30
tan 60
Geometry B
Unit 5
Lesson 3 Practice
Name
Fill in the missing angle in each triangle.
Also, find the missing sides in each right triangle. Round each answer to the nearest hundredth (two
decimal places). You must show work that shows how you got your answer.
1.
3.
2.
4.
5. A jump ramp for waterskiing makes an angle of 15° with the surface of the water. The ramp rises 1.58
meters above the surface. What is the length of the ramp (the diagonal)? Round to two decimal places.
Draw right ABC with the given dimensions. Angle C is the right angle.
Fill in the missing angle in each triangle.
Also, find the missing sides in each right triangle. Round each answer to the nearest hundredth (two
decimal places). You must show work that shows how you got your answer.
Verify your side lengths are correct by measuring.
5. B = 36°, a = 3.6 cm
6. A = 72°, c = 5.1 cm
Geometry B
Unit 6
Lesson 4 Practice
1. Using your calculator, find the following rounded to the nearest tenth of a degree. Be sure your
calculator is in degree mode.
2. Find the missing angle in each triangle. Round to the nearest tenth of a degree.
3. Solve the triangle. Round angles to the nearest tenth and sides to the nearest hundredth.
4. Draw right ABC with the given dimensions. Angle C is the right angle.
Solve the triangle. Round angles to the nearest tenth and sides the nearest hundredth.
a = 2.6 cm, b = 3.6 cm
b = 1.8 cm, c = 6.2 cm
Geometry B
Unit 6
Lesson 5 Practice
Name
1. Classify each angle as an angle of elevation or an angle of depression.
1
2
3
4
2. The Seattle Space Needle casts a 67-meter shadow. If the angle of elevation from the tip of the
shadow to the top of the Space Needle is 70º, how tall is the Space Needle? Round to the nearest
meter.
3. Suppose the plane is at an altitude of 3500 ft and the angle of elevation from the airport to the plane
is 29°. What is the horizontal distance between the plane and the airport? Round to the nearest foot.
4. A restaurant needs to build a wheelchair ramp for its customers. The angle of elevation for a ramp is
recommended to be 5  . If the vertical distance from the sidewalk to the front door is two feet, what is
the horizontal distance that the ramp will take up? How long will the ramp be? Round your answers to
the nearest hundredth.
5. A forest ranger in a 120 foot observation tower sees a fire. The angle of depression to the fire is 3.5°.
What is the horizontal distance between the tower and the fire? Round to the nearest whole number.
6. Marion is observing the launch of a space shuttle from the command center. When she first sees the
shuttle, the angle of elevation to it is 16°. A short time later, the angle of elevation is 74°. How far has
the shuttle traveled? (Hint: You will have to find the height of the shuttle at each angle of elevation.)
Geometry B
Unit 6
Lesson 8 Practice
Name
1) Using your special right triangles, fill in the angles and coordinates on the unit circle.




,
,



,
,

,
y



,


,



,


,
x


,


,


,



,

,


,
,


2) On the unit circle, all angles start at the
________________________________.
3) On the unit circle, the y-coordinate is the value of the
______________ of the angle.
4) On the unit circle, the x-coordinate is the value of the
______________ of the angle.
5) What other three angles refer to an angle of 65°?
6) Draw each angle on the unit circle to the right.
7) At 50°, the value of the coordinate is (.6428, .7660). Without a calculator, find the values of the
following.
cos 50° =
cos130° =
cos 230° =
cos 310° =
sin 50° =
sin130° =
sin 230° =
sin 310° =
Geometry B
Unit 6
Lesson 6 Practice
Name
Use the Law of Sines to find all angles or side lengths. Round side lengths to two decimal places and
angles to one decimal place. Write your answers on the diagram.
Draw ABC : A = 35°, b = 2.5
cm, C = 70°
Geometry B
Unit 6
Lesson 7 Practice
Name
Use the Law of Cosines to find all angles and side lengths. Round side lengths to two decimal places
and angles to one decimal place. Write your answers on the diagram.
Draw ABC : a = 4.1 cm, b = 2.5
cm, C = 70°