Lesson%2026%20-%20Review%20of%20Right%20Triangle%20Trigonometry

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Lesson 26 - Review of Right Triangle Trigonometry

• PreCalculus Santowski

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(A) Review of Right Triangle Trig

• Trigonometry is the study and solution of
  Triangles. Solving a triangle means finding the
  value of each of its sides and angles. The
  following terminology and tactics will be
  important in the solving of triangles.
• Pythagorean Theorem (a2b2c2). Only for right
  angle triangles
• Sine (sin), Cosecant (csc or 1/sin)
• Cosine (cos), Secant (sec or 1/cos)
• Tangent (tan), Cotangent (cot or 1/tan)
• Right/Oblique triangle

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(A) Review of Right Triangle Trig

• In a right triangle, the primary trigonometric
  ratios (which relate pairs of sides in a ratio to
  a given reference angle) are as follows
• sine A opposite side/hypotenuse side the
  cosecant A cscA h/o
• cosine A adjacent side/hypotenuse side the
  secant A secA h/a
• tangent A adjacent side/opposite side the
  cotangent A cotA a/o
• recall SOHCAHTOA as a way of remembering the
  trig. ratio and its corresponding sides

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(B) Review of Trig Ratios

• Evaluate and interpret
• (a) sin(32)
• (b) cos(69)
• (c) tan(10)
• (d) csc(78)
• (e) sec(13)
• (f) cot(86)

• Evaluate and interpret
• (a) sin(x) 0.4598
• (b) cos(x) 0.7854
• (c) tan(x) 1.432
• (d) csc(x) 1.132
• (e) sec(x) 1.125
• (f) cot(x) 0.2768

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(C) Review of Trig Ratios and Triangles

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(C) Review of Trig Ratios and Triangles

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(B) Examples Right Triangle Trigonometry

• Using the right triangle trig ratios, we can
  solve for unknown sides and angles
• ex 1. Find a in ABC if b 2.8, C 90, and A
  35
• ex 2. Find A in ABC if c 4.5 and a 3.5 and B
  90
• ex 3. Solve ABC if b 4, a 1.5 and B 90

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(B) Review of Trig Ratios

• If sin(x) 2/3, determine the values of cos(x)
  tan(x)
• If cos(x) 5/13, determine the value of sin(x)
  tan(x)
• If tan(x) 5/8, determine the sum of sin(x)
  2cos(x)
• If tan(x) 5/9, determine the value of sin2(x)
  cos2(x)
• A right triangle with angle a 30? has an
  adjacent side X units long. Determine the
  lengths of the hypotenuse and side opposite a.

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Examples Right Triangle Trigonometry

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Examples Right Triangle Trigonometry

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(E) Examples Right Triangle Trigonometry

• A support cable runs from the top of the
  telephone pole to a point on the ground 43 feet
  from its base. If the cable makes an angle of
  32.98º with the ground, find (rounding to the
  nearest tenth of a foot)
• a. the height of the pole
• b. the length of the cable

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(E) Examples Right Triangle Trigonometry

• Mr Santowski stands on the top of his apartment
  building (as part of his super-hero duties, you
  know) and views a villain at a 29º angle of
  depression. If the building I stand upon is 200 m
  tall, how far is the villain from the foot of the
  building?

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(E) Examples Right Triangle Trigonometry

• You are hiking along a river and see a tall tree
  on the opposite bank. You measure the angle of
  elevation of the top of the tree and find it to
  be 46.0º. You then walk 50 feet directly away
  from the tree and measure the angle of elevation.
  If the second measurement is 29º, how tall is the
  tree? Round your answer to the nearest foot.

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Examples Right Triangle Trigonometry

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Examples Right Triangle Trigonometry

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Examples Right Triangle Trigonometry

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Examples Right Triangle Trigonometry

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Examples Right Triangle Trigonometry

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Examples Right Triangle Trigonometry

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Examples Right Triangle Trigonometry

• (8) While driving towards a mountain, Mr S
  notices that the angle of elevation to the peak
  is 3.5º. He continues to drive to the mountain
  and 13 miles later, his second sighting of the
  mountain top is 9º. Determine the height of the
  mountain.

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Examples Right Triangle Trigonometry

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Examples Right Triangle Trigonometry