Today – Wednesday, February 27, 2013

Return HW #4 and correct

Review: Trigonometric Ratios (SOH CAH TOA)

Review Practice: In Class-Due Today!

Learning Target : Use trigonometric ratios to solve for missing sides of a triangle.

Independent Practice

Review HW #4:

45-45-90 and 30-60-90Special Triangles

TRIGONOMETRIC RATIOS:

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑙𝑒𝑔

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑙𝑒𝑔

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃

OPPOSITE SIDE: Given an angle of a triangle, the opposite side is the side opposite of that angle.

ADJACENT SIDE: Given an angle of a triangle, the adjacent side is next to/beside that angle.

HYPOTENUSE: The hypotenuse is the side of the triangle that connect the two legs of the triangle.

TRIGONOMETRIC RATIOS:

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃

“”𝑆𝐼𝑁𝐸 : 𝑠𝑖𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝑂𝐻

𝐶𝑂𝑆𝐼𝑁𝐸 :𝑐𝑜𝑠 𝜃=𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝐴𝐻

𝑇𝐴𝑁𝐺𝐸𝑁𝑇 :𝑡𝑎𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

=𝑂𝐴

𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨

4

3 5

PRACTICE: Given the sides of the right triangle, find the trigonometric ratios: .

𝑠𝑖𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝑂𝐻

=35

𝑐𝑜𝑠𝜃=𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝐴𝐻

=45

𝜃

𝑡𝑎𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

=𝑂𝐴

=34

“”

𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨

Review Practice:

45-45-90 and 30-60-90Special Triangles

and

Trigonometric Ratios

IN CLASS-DUE TODAY!

TANGENT RATIO:

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃

𝑇𝐴𝑁𝐺𝐸𝑁𝑇 :𝑡𝑎𝑛𝜃=h𝑙𝑒𝑛𝑔𝑡 𝑜𝑓 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒h𝑙𝑒𝑛𝑔𝑡 𝑜𝑓 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

=𝑂𝐴

𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨

Solving for tangent ratios: substitute known values, solve for unknown variable and evaluate.

121

𝑛

PRACTICE: Find n using the tangent ratio. Round answer to the nearest tenth.

52 °

Use tangent ratio

Substitute known values

Multiply by 121 on both sides

Solve for n using calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

𝑥

52

PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.

26 °

Use tangent ratio Substitute known values Multiply by x on both sides

Divide by , both sides Solve for x using a calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

SINE RATIO:

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃

𝑆𝐼𝑁𝐸 : 𝑠𝑖𝑛𝜃=h𝑙𝑒𝑛𝑔𝑡 𝑜𝑓 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒h𝑙𝑒𝑛𝑔𝑡 𝑜𝑓 h 𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝑂𝐻

𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨

Solving for tangent ratios: substitute known values, solve for unknown variable and evaluate.

67 𝑥

PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.

46 °

Use sine ratio

Substitute known values

Multiply by 67 on both sides

Solve for n using calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

45𝑥

PRACTICE: Find x using the sine ratio. Round answer to the nearest tenth.

41°

Use sine ratio Substitute known values Multiply by x on both sides

Divide by , both sides Solve for x using a calculator

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒

COSINE RATIO:

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃

𝐶𝑂𝑆𝐼𝑁𝐸 :𝑐𝑜𝑠 𝜃=h𝑙𝑒𝑛𝑔𝑡 𝑜𝑓 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒h𝑙𝑒𝑛𝑔𝑡 𝑜𝑓 h 𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝐴𝐻

𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨

Solving for tangent ratios: substitute known values, solve for unknown variable and evaluate.

40

𝑥

PRACTICE: Find x using the cosine ratio. Round answer to the nearest tenth.

65 °

Use cosine ratio Substitute known values Multiply by x on both sides

Divide by , both sides Solve for x using a calculator

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

𝑥17

PRACTICE: Find x using the cosine ratio. Round answer to the nearest tenth.

63 °

Use tangent ratio

Substitute known values

Multiply by 17 on both sides

Solve for n using calculator

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

Solve for x using 𝑥

6

PRACTICE: Find x and y using the tangent ratio. Round answer to the nearest tenth.

52 ° h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒

𝑦𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

Solve for y using

HOMEWORK #5:

Pg. 470: 18-20, 24-29, 31, 32Pg. 477: 10-15, 18-27

If finished, work on other assignments:

HW #1: Pg. 436: 3-29 oddHW #2: Pg. 444: 1-6, 8, 10, 12HW #3: Pg. 461: 3-18HW #4: 7.4 Special Triangles WS (Kuta)