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5.2 Applications of Right Triangles Tues Dec 17

5.2 Applications of Right Triangles Tues Dec 17. Do Now Find the 6 trig values for 30 degrees. HW Review p.444 any. Solving Right Triangles. To solve a triangle means to find the lengths of all sides and the measures of all angles

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5.2 Applications of Right Triangles Tues Dec 17

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  1. 5.2 Applications of Right TrianglesTues Dec 17 Do Now Find the 6 trig values for 30 degrees

  2. HW Review p.444 any

  3. Solving Right Triangles • To solve a triangle means to find the lengths of all sides and the measures of all angles • Typically, upper-case letters represent the angles of a triangle (ABC) and lower-case letters represent the side opposite the angle • Side a is opposite angle A

  4. Ex1 • Solve the triangle ABC given: • C is a right angle • A is 61.7 degrees • Side c = 106.2

  5. Ex2 • Solve triangle DEF given: • E is a right angle • Side f = 13 • Side e = 23

  6. Applications – Ex1 • A backpacker hiking east along the North Rim of the Grand Canyon notices an unusual rock formation directly across the canyon. She decides to continue watching the landmark while hiking along the rim. In 2 hr, she has gone 6.2 mi due east an the landmark is still visible but at a 50 degree angle. • A) How many miles is she from the rock formation? • B) How far is the formation from her starting point?

  7. Angle of Depression / Elevation • The angle between the horizontal and a line of sight above the horizontal is the angle of elevation • The angle between the horizontal and a line of sight below the horizontal is called the angle of depression

  8. Ex2 • In Telluride, Colorado, there is a free gondola ride that begins in town at an elevation of 8725 ft that travels 5750 ft to Station St. Sophia, whose altitude is 10,550 ft. What is the angle of elevation from the town to St. Sophia?

  9. Ex3 • To measure cloud height at night, a vertical beam of light is directed on a spot on the cloud. From a point 135 ft away from the light source, the angle of elevation to the spot is found to be 67.35 degrees. Find the height of the cloud.

  10. Bearing • One method of giving direction, or bearing, involves reference to a north-south line using an acute angle. • Ex: N55W means 55 degrees west of a line going north

  11. Ex4 • A forest ranger at point A sights a fire directly south. A second ranger at point B, 7.5 mi east, sights the same fire at a bearing of S 27.38deg W. How far from A is the fire?

  12. Ex5 • At a baseball field, the angle of depression from a seat in highest row to home plate is 29.9 degrees, and the angle of depression to the pitcher’s mound is 24.2 degrees. The distance between home plate and the pitcher’s mound is 60.5 ft. • (A) Find the viewing distance to home plate • (B) Find the viewing distance to the pitcher’s mound

  13. Closure • Solve triangle ABC given: • Angle C is a right angle • Angle B is 45 degrees • Side c = 10 • HW: p.454 #1-37 odds • Quiz Thurs or Fri

  14. 5.1-5.2 ReviewWed Dec 18 • Do Now • From the top of a lighthouse 55ft above sea level, the angle of depression to a small boat is 11.3 degrees. How far from the foot of the lighthouse is the boat?

  15. HW Review p.454 #1-37

  16. 5.1-5.2 Review • 5.1 Trigonometric Functions • 6 Trig Functions • 30-60-45 degree trig values (exact value) • Cofunction and Reciprocal Identities • 5.2 Applications of Right Triangles • Solving Right Triangles • Solving word problems using right triangles and trigonometry

  17. Closure • What are the trigonometric functions? How are they related? What are some applications? • Quiz tomorrow

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