Trigonometry Section 3 – Solve Application Problems using Right Triangle Trigonometry

Applications Measuring inaccessible lengths Height of a building (tree, tower, etc.) Width of a river (canyon, etc.)

Terminology Angle of Elevation  A

Terminology Angle of Depression  A

Application: Height To establish the height of a building, a person walks 120 ft away from the building. At that point an angle of elevation of 32  is formed when looking at the top of the building. Example 1 of 4

Application: Height  32  120 ft h = ? Example 1 of 4 H = ft To establish the height of a building, a person walks 120 ft away from the building. At that point an angle of elevation of 32  is formed when looking at the top of the building.

Application: Height  68  h = ? 55 ft Example 2 of 4 H = ft An observer on top of a hill measures an angle of depression of 68  when looking at a truck parked in the valley below. If the truck is 55 ft from the base of the hill, how high is the hill?

Surveying

Application: Surveying ? 70 ft 37  Example 3 of 4 D = 52.7 ft

Application: Surveying Road has a grade of 5.5%. Convert this to an angle expressed in degrees.  100 ft 5.5 ft ?  Example 4 of 4 A = 3.1 

Practice Set 17 Pages 59-61

Trigonometry - Section 3 Solving problems with no right triangles.

Review

Example 1 Determine the height of this isosceles triangle. 40  15 ft height = ? h = 6.3 ft

Example 2 Determine the length of side x in this equilateral triangle. height = 48 ” x x = 55.4 ”

Practice Set 18 Page

Trigonometry – Section 3 Additional Technical Applications

Application 1 Determine the depth d of the groove machined in this steel block. 82  d 3”3” 1.1 ” d = 0.46 ” 0.8 ” 41  0.4 ” 41  d 0.4 ”

Application 2 Determine the total length of steel needed to make this frame. 11 ft 35  h = 3.85 ft, Total = 11 ft ft ft ft = ft

Application 3 Determine the taper angle of this steel shaft. t 145 mm 40 mm 22 mm A  t = 7.1 

Application 4 The diagram shows a bolt circle. Determine the distance x between the centers of any two bolt hole locations x radius 2.4 ”

Application x radius 2.4 ” x =4.16 ”

Terminology: Tangent Tangent Line tangent line tangent point

Property + 90  radius + +

Angle outside a circle + 34  17 

Putting it all together + 40  20  1.4 ft dia. 0.7 ft radius 0.7 ft 20 

Example: Illustration + 64  0.8 ” dia. 0.4 ” 32 

Example: Illustration 36  0.5 ” dia ” 18 

Example: Solve A gauge pin is placed in a machined groove as shown. Determine the length of dimension x  8 mm dia. x

Example: Solve + 8 mm dia. 32  x x = 6.4 mm + 4 mm = 10.4 mm

Piston Travel 3.5 ” 290 

Piston Travel  290  3.5 ” 1.75 ” 70  ” 1.75 ” 70  1.75 ” – ” = ”

Practice Set 19 Pages 73-75

What ’ s Next? Quizzes 1 -3 pages 76 – 83 Chapter Test on Trigonometry