Name: _________________________________________________________ 14-12 Trig Review (Unit 9) Geometry Pd. ______ Date: __________

14-12: Trigonometry Review

Concept 1: Trig Ratios - SohCahToa

Key Ideas/Tips Regents Examples/ MY NOTES 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(sin ) = sin-1(

)

sin-1(sin ) = sin-1(

)

= 53.1° *Angle of Elevation – angle formed from ground up

*Angle of Depression – angle formed from eye-level down

The The diagram below shows two

similar triangles. If

, what is

the value of to the nearest tenth?

(1) (2) (3) (4)

Concept 2: Law of Sines

Key Ideas/Tips Regents Examples/ MY NOTES 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” (the angles and sides across from each other)

In the

What is the distance from campsite A to campsite B, to the

nearest yard?

1) 1,469

2) 1,150

3) 2,140

4) 2,141

5.6

Concept 3: Law of Cosines

Key Ideas/Tips Regents Examples/ MY NOTES Law of Cosines **NEED TO USE THE ANGLE OPPOSITE “a2.”

Law of Cosines can be used if...

you have 3 sides and 1 angle of a triangle, including the unknown.

Find the size of the smallest angle to the nearest degree.

Concept 4: Cofunctions

Key Ideas/Tips Regents Examples/ MY NOTES Cofunctions

Try it! Write a trig function equivalent to the following, but with an angle value less than 45 = cos ( ) When asked to explain: When two angles are complementary, the value of the sine of one angle is equal to the value of the cosine of the other angle.

2. In , the complement of is

. Which statement is always true?

1) 2) 3) 4)

Find

2. Find the value of R that will make the equation

true when . Explain your

answer.

Self-Assess: Where should you start?

Rank the following concepts with 1-4, where 1 = “I feel the most confident with this topic!” And 4 = “I feel the

least comfortable with this topic.”

Concept 1 Concept 2 Concept 3 Concept 4

Concept 1: Right Triangle Trig Ratios SOHCAHTOA – CALCULATOR in DEGREE MODE!!!!!!

1. Which ratio represents the cosine of angle A in the right triangle below? 1)

2)

3)

4)

2. In triangle MCT, the measure of , , , and . Which ratio represents the sine

of ? (Hint: DRAW IT!) 1)

2)

3)

4)

Complete both Column A AND Column B:

Column A Column B

5. Solve for the value of x, to the nearest tenth.

8. Solve for the to the nearest hundredth of a

degree

x

16

7. A tree casts a 25-

foot shadow on a

sunny day, as

shown in the

diagram below

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?

10. 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.

To the nearest tenth of a degree

what is the measure of angle x?

Concept 2: Law of Sines ***IMPORTANT! You will NOT BE GIVEN these equations on the test. You have to memorize each.

11. Given triangle ABC, m Find the measurement of to the nearest degree.

12. Given triangle , , , , and , find to the nearest whole

number.

Concept 3: Law of Cosines

13. Find the largest angle, to the nearest tenth of a degree, of a triangle whose sides are 9, 12 and 18

14. 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.

Concept 4: Cofunctions

Solve the following problems using your knowledge of cofunctions:

15. 15.

16. Explain how you got your answer.

17. If Cos A = 2x + 57 and Sin B = 5x in right triangle ABC, find the value of x. Explain how you got your

answer.

Jumbled Jamboree 18. A telephone pole is anchored by two support cables, ̅̅ ̅̅ ̅̅ ̅̅ in the figure below. Point is m from the base of the tower, and .

The building commissioner of Harrison would like to build a box to hold the loose wires at the top of the poll.

To do this, he must know the length from B to D. He selected HHS Geometry students to find this information

out for him.

Solve for the distance to the nearest hundredth of a meter from B to D.

19. 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 , determine the height of the water tower (from A to E) to the

nearest whole number.

20. The two triangles below are similar. Given that Sin =

, what is the value of x to the nearest 10th.