TODAY IN GEOMETRY… Review: Methods solving for missing sides of a right triangle Learning...
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Transcript of TODAY IN GEOMETRY… Review: Methods solving for missing sides of a right triangle Learning...
TODAY IN GEOMETRY…
Review: Methods solving for missing sides of a right triangle
Learning Target: 7.6 Finding an angle using inverse Trigonometry
Independent Practice
Basic Trig Problems in 3 categories:
• Pythagorean Theorem• Special Right Triangles:
30-60-9045-45-90
• Trig Ratios: Sin, Cos, Tan
𝑥6
PRACTICE: Identify what category this problem lies in (Pythagorean, Special Right Triangles, or Trig Ratios). Solve for the missing variables.
30 °𝑦
Substitute known values
Multiply Divide
Substitute known values
Simplify
Special Right Triangle
𝑎
17.821.2
PRACTICE: Identify what category this problem lies in (Pythagorean, Special Right Triangles, or Trig Ratios). Solve for the missing variable.
The unknown side is attached to the right angle so it is a leg of the triangle.
Use the Pythagorean theorem to find the missing leg:
Given two sides:Pythagorean Theorem
19𝑥
PRACTICE: Identify what category this problem lies in (Pythagorean, Special Right Triangles, or Trig Ratios). Solve for the missing variable.
48 ° Use sine ratio
Substitute known values Multiply by x on both sides
Divide by , both sides Solve for x using a calculator
h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒Given one side and an angle:
Trig Ratios
30 °4
𝑦
Which method would you use to find the missing sides of the right triangle (Pythagorean Theorem, Special Right Triangles, or Trig)?
𝑥
652 ° 𝑦 𝑥8
7
Find Trigonometric angles using inverse
𝜃𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
TRIGONOMETRIC RATIOS:
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃
“”𝑆𝐼𝑁𝐸 : 𝑠𝑖𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
=𝑂𝐻
𝐶𝑂𝑆𝐼𝑁𝐸 :𝑐𝑜𝑠 𝜃=𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
=𝐴𝐻
𝑇𝐴𝑁𝐺𝐸𝑁𝑇 :𝑡𝑎𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
=𝑂𝐴
𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨
METHOD TO FIND TRIG ANGLES:
𝑜𝑝𝑝𝑜
𝑠𝑖𝑡𝑒 h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃
“”
θ=𝑡𝑎𝑛− 1(𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 )
𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨
1. Find the opposite, adjacent and hypotenuse of your right triangle.
θ=𝑐𝑜𝑠− 1( 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 )
θ=𝑠𝑖𝑛− 1( 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 )
2. Use the trig function that contains the sides of your triangle.3. Use the inverse trig function to calculate the angle.
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 #7:
Pg. 485: 3-8, 10-18
If finished, work on other assignments:
HW #1: Pg. 436: 3-29 oddHW #2: Pg. 444; 1-6, 8, 10, 12HW #3: Pg. 461: 3-18IN CLASS WORK #4: 7.4 Special Right Triangles WSHW #5: 7.5 WS-x on topHW #6: 7.5 WS-x on bottom