Download unit 9 review packet

Name: _________________________________________________________
Geometry Pd. ______
Unit 9: Trigonometry
9-1
9-2
Unit 9 Review
Date: __________
Trigonometric Ratios – SOHCAHTOA ****PUT
CALCULATOR IN DEGREES***
- Used to solve for sides or to solve for angles
-
When solving for a side remember to use: sine,
cosine, or tangent and cross multiply!
-
When solving for an angle remember to use:
sine inverse, cosine inverse, or tangent inverse
ex) sin-1(sin𝜃) =
sin-1(sin𝜃)
4
sin-1( )
=
𝜃 = 53.1°
5
4
sin-1(
)
5
*Angle of Elevation – angle formed from ground up
9-4
9-5
*Angle of Depression – angle formed from eye-level down
Law of Sines
Tip: Read carefully, if it is NOT a right triangle we can’t use SOHCAHTOA!

o
o The Law of Sines can be used to find...

you have 2 sides and 2 angles of a triangle, including the unknown.
Must find the “pairs,” or the angles and sides across from each other
Law of Coines
**NEED TO USE THE ANGLE OPPOSITE “a2.”

9-7
Law of Cosines can be used if...
 you have 3 sides and 1 angle of a triangle, including the unknown.
Cofunctions
sin 𝜃 = cos(90 − 𝜃)
cos 𝜃 = 𝑠𝑖𝑛(90 − 𝜃)
Try it! Write a trig function equivalent to the following, but with an angle value less than 45°
sin 78 = cos(90 − 78) = cos (12)
Station 1: Pythagorean Theorem
1. A ladder 25 feet long is leaning against a wall 20 feet up the wall. How far is the bottom of the ladder from the
bottom of the wall?
1. Draw it
2. Show all work to support your answer
2. In the accompanying diagram of right triangles ABD and DBC,
leave answer in simplest radical form.
,
, and
Station 2: SOHCAHTOA – CALCULATOR in DEGREE MODE!!!!!!
3. Which ratio represents the cosine of angle A in the right triangle below?
1)
2)
3)
4)
. Find the length of
,
4. In triangle MCT, the measure of
of
? (Hint: DRAW IT!)
1)
,
,
, and
. Which ratio represents the sine
2)
3)
4)
5. The diagram below shows right triangle LMP.
Which ratio represents the tangent of
1)
?
2)
3)
4)
6. Which equation shows a correct trigonometric ratio for angle A in the right triangle below?
1)
2)
3)
4)
Complete both Column A AND Column B:
Column A
7. Solve for the value of x, to the nearest tenth.
x
16
Column B
8. Solve for the 𝑚∡𝐵 to the nearest hundredth of a
degree
9. You go to the park on a windy day to fly a kite. You
have released 40 feet of string. The string makes an
angle of 36° with the ground. How high is the kite in the
air to the nearest foot?
10. A ladder is resting against the side of a building. The
bottom of the ladder is 12 feet from the building, and
the ladder reaches 7 feet up the side of the building.
Find the measure of the angle of elevation, to the
nearest tenth of a degree.
11. A tree casts a 25-foot shadow on a sunny day, as
shown in the diagram below
12. The diagram below shows the path a bird flies from
the top of a 9.5 foot tall sunflower to a point on the
ground 5 feet from the base of the sunflower.
If the angle of elevation from the tip of the shadow to
the top of the tree is 32°, what is the height of the tree to
the nearest tenth of a foot?
To the nearest tenth of a degree what is the measure of
angle x?
13. ****What’s the difference between problems in column A vs. Column B?
Station 3: Cofunctions
Solve the following problems using your knowledge of cofunctions:
14.
15.
16. If sin 6𝐴 = cos 9𝐴 , then A is equal to:
17.
Explain how you got your answer.
18. If Cos A = 2x + 57 and Sin B = 5x in Triangle ABC, find the value of x. Explain how you got your answer.
1
19. The degree measure of an angle in a right triangle is x, and sin x = 3. Which of the following are also
1
equal to 3.
1) cos x
2) cos (x -90)
3) cos (90-x)
4) sin(90 +x)
Station 4: Law of Sines and Cosines
***IMPORTANT! You will not be GIVEN these equations on the test. You have to memorize each.
20. Find the largest angle, to the nearest tenth of a degree, of a triangle whose sides are 9, 12 and 18
21. For the figure below, m∠ ADB and m∠ C to the nearest whole degree.
22. The playground at a day-care center has a triangular-shaped sandbox. Two of the sides measure 25 feet
and 18.5 feet and form an included angle of 52°. Find the length of the third side of the sandbox to the
nearest tenth of a foot.
a. Which law do we use here?
b. Solve for the third side of the sandbox.
23. Given triangle𝐷𝐸𝐹, ∠𝐷 = 22°, ∠𝐹 = 91°, 𝐷𝐹 = 16.55, and 𝐸𝐹 = 6.74, find 𝐷𝐸 to the nearest hundredth.
Station 5: Jumbled Jamboree
24.
The water tower in the picture below is modeled by the two-dimensional figure beside it. The water tower
is composed of a hemisphere, a cylinder, and a cone. Let C be the center of the hemisphere and let D be the
center of the base of the cone.
If
feet,
feet, and
nearest whole number.
, determine the height of the water tower (from A to E) to the
2
25. The two triangles below are similar. Given that Sin𝜃 = 7, what is the value of x to the nearest 10th.
26. The diagram shows rectangle ABCD, with diagonal BD.
27.
28.