Lesson 33 - Applications of Right Triangle Trigonometry

1
Lesson 33 - Applications of Right Triangle
Trigonometry

• IB Math SL1 Santowski

2
(A) Review of Right Triangles

• 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
• cosine A adjacent side/hypotenuse side
• tangent A opposite/adjacent side side
• recall SOHCAHTOA as a way of remembering the
  trig. ratio and its corresponding sides

3
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

4
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?

5
Examples Right Triangle Trigonometry

6
Examples Right Triangle Trigonometry

7
Examples Right Triangle Trigonometry

8
Examples Right Triangle Trigonometry

• (6) Assuming that the Earth has a radius of 6380
  km, determine the length of the 35th parallel.
• (7) To determine the width of a river, a surveyor
  marks a point on the bank of the river, A. Her
  partner is standing directly across the river
  from her at point C. The surveyor then walks 100
  m downstream to point B, where she now has a line
  of sight to her partner at an angle of 58º
  relative to the river bank. Determine the width
  of the river.

9
Examples Right Triangle Trigonometry

10
Examples Right Triangle Trigonometry

11
Examples Right Triangle Trigonometry

12
Examples Right Triangle Trigonometry

13
Examples Right Triangle Trigonometry

14
Examples Right Triangle Trigonometry

15
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.

16
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.

17
Examples Right Triangle Trigonometry

18
Examples Right Triangle Trigonometry

19
Examples Right Triangle Trigonometry

20
(G) Homework

• 10CDEF - Right Angled Trig Review
• HW
• Ex 10C 1be, 2, 5, 6
• Ex 10D 1ae, 3c, 4b, 5b, 6a, 7ac, 11,12
• Ex 10E 2, 6, 8
• Ex 10F 1bc, 2b,3a