Do-Now

3

2

7

3

8

8

1. Use the Pythagorean Theorem to solve the following problem.

Firefighters have a 17 foot extension ladder. In order to reach 15 feet up a building, how far away from the building should the foot of the ladder be placed?

Convert each fraction to a decimal. Round to four decimal places.

2. 3. 4.

9.7-9.8: Trigonmetric Ratios9.7-9.8: Trigonmetric Ratios9.7-9.8: Trigonmetric Ratios9.7-9.8: Trigonmetric RatiosObjective: use sine, cosine and tangent Objective: use sine, cosine and tangent ratios to find side lengths of trianglesratios to find side lengths of triangles

Homework:Homework:

9.7-9.8 Practice Worksheet9.7-9.8 Practice Worksheet

Trigonometry

• The ratio of lengths of two sides of a right triangle

• You can only take the sine, cosine, and tangent of one of the acute angles of a right triangle.

• Real-life connection: Architecture, landscaping, construction, etc. (careers that use math, science and

• engineering)

Vocabulary to understand:

HypotenuseOppositeAdjacent

ZYsin

XYX

X

YZ

Finding lengths: Make sure calculator is in Radian mode not Degree

Sine (abbreviation: sin)

XZsin

XYY

ZYsin

XYX

hypotenuse

leg oppositesin

X

YZ

XY

ZYX sin

*The opposite side is always across from the given angle.* The hypotenuse is always the side opposite of the right angle.

Cosine (abbreviation: cos)

ZYcos

XYY

cosXY

XZX

X

YZ

hypotenuse

legadjacent cos

* The adjacent side is always next to or attached to the angle that is identified. It cannot be the hypotenuse.

Tangent (abbreviation: tan)

XZtan

ZYY

ZYtan

XZX

X

YZ

legadjacent

leg oppositetan

SOHCAHTOAsin

sin

cos

cos

tan

tan

A

B

A

B

A

B

3

5

4

3

1.)

2.)

3.)

4.)

5.)

6.)

A

BC

35

4

3

4

4

5

4

5

3

5

sin =

cos =

tan =

Describe how the measures of two legs are related if the tangent of one of the acute angles is = 1.

Use your calculator and round to the nearest

hundredth.1.) sin 43

o =

2.) cos 72o =

3.) tan 35o =

Solve for the variable.1. Start by asking yourself, what sides are the numbers

and variables in relation to the given angle measure (adjacent side, opposite side or hypotenuse)?

2. Then ask, which trig function uses the sides you identified?

3. Set up the ratios based on S O H C A H T O A.

opposite

hypotenuse

opposite

adja

centhypotenuse

adja

cent

Solve for the variable.When the variable is on the bottom,

divide (# ÷ trig function).When the variable is on the top,

multiply (# x trig function).

x

3

10

bTan 22˚= Cos 32˚= Sin 28˚=

15

a

3 ÷ Tan 20 = 10 x Cos 32 = 15 x Sin 28 =

Real-life ConnectionA surveyor is finding the width of a river for a proposed bridge. A theodolite is used by the surveyor to measure angles. The distance from the surveyor to the proposed bridge site is 40 feet. The surveyor measures a 50 angle to the bridge site across the river. Find the length of the bridge to the nearest foot.

Review:Find the following and write the answers as fractions in simplest form and as decimals rounded to the four decimal places.

1. Sin P =

2. Cos P =

3. Tan P =

Find the lengths of the legs. Round your answer to four decimal places.

4. 5.