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TODAY IN GEOMETRY…
Review: SOH CAH TOA
Learning Target 1: 7.4 You will find missing sides of a triangle using TRIG
Independent Practice
Learning Target 2: 7.4 You will find missing angles of a triangle using INVERSE TRIG
CH.7 QUIZ 2-MONDAY/TUESDAY!
4
3 5
PRACTICE: Given the sides of the right triangle, find all the trigonometric ratios.
𝑠𝑖𝑛𝐶=𝑂𝐻
𝑐𝑜𝑠𝐶=𝐴𝐻
𝑡𝑎𝑛𝐶=𝑂𝐴
“”
𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨
𝐴
𝐵
𝐶
¿
¿
¿
𝑠𝑖𝑛𝐵=𝑂𝐻
𝑐𝑜𝑠 𝐵=𝐴𝐻
𝑡𝑎𝑛𝐵=𝑂𝐴
¿
¿
¿
35
4534
453543
5
12 13
PRACTICE: Given the sides of the right triangle, find all the trigonometric ratios for angle C.
𝑠𝑖𝑛𝐶=𝑂𝐻
𝑐𝑜𝑠𝐶=𝐴𝐻
𝑡𝑎𝑛𝐶=𝑂𝐴
“”
𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨
𝐴
𝐵
𝐶
¿
¿
¿
1213
513125
Use Pythagorean theorem to find the missing side:
MULTIPLY: when x is on topExample:
DIVIDE: when x is on bottomExample:
121
𝑛
PRACTICE: Find n using the tangent ratio. Round answer to the nearest tenth.
52 °
Use tangent ratio
Substitute known values
Variable on top (multiply)
Solve for n using calculator
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒
67 𝑥
PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.
46 °
Use sine ratio
Substitute known values
Variable on top (multiply)
Solve for x using calculator
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
45𝑥
PRACTICE: Find x using the sine ratio. Round answer to the nearest tenth.
41°
Use sine ratio Substitute known values Variable on bottom (divide)
Solve for x using a calculator
h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒
40
𝑥
PRACTICE: Find x using the cosine ratio. Round answer to the nearest tenth.
65 °
Use cosine ratio
Substitute known values Variable on bottom (divide)
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 cosine ratio
Substitute known values
Variable on top (multiply)
Solve for x using calculator
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑥
52
PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.
26 °
Use tangent ratio Substitute known values Variable on bottom (divide)
Solve for x using a calculator
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒
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:
Finding missing sides using TRIG WS
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: Intro to TRIG WS
Find Trigonometric angles using inverse
𝜃𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
INVERSE TRIG:
θ=𝑡𝑎𝑛− 1(𝑂𝐴 )θ=𝑐𝑜𝑠− 1( 𝐴𝐻 )θ=𝑠𝑖𝑛− 1( 𝑂𝐻 )
13
14
PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth.
𝑥
Use tangent ratio
Substitute known values Use inverse tangent
Solve for x using calculator
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒
2436
PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth.
𝑥
Use cosine ratio
Substitute known values
Use inverse cosine
Solve for x using calculator
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
43
92
PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth.
𝑥
Use sine ratio
Substitute known values
Use inverse sine
Solve for x using calculator
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒
h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Solve for x using 8
6
PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth.
𝑥 h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒10
Solve for y using
𝑦
There are multiple ways to solve this problem, you may
choose any trig function because all sides are given!
HOMEWORK #6:
Finding missing angles using TRIG WS
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: Intro to TRIG WSHW #5: Finding missing sides using TRIG WS
