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Right Triangles and Trig Ratios. Section 14.3. Basic Ratios. We can use basic trig ratios to solve for missing parts of right triangles Ratios do not depend on the size of the triangle, but on the acute angles The six trig ratios are: sin θ = opposite/ hyp csc θ = hyp /opposite

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basic ratios
Basic Ratios
  • We can use basic trig ratios to solve for missing parts of right triangles
  • Ratios do not depend on the size of the triangle, but on the acute angles
  • The six trig ratios are:

sin θ = opposite/hypcsc θ = hyp/opposite

cos θ = adjacent/hyp sec θ = hyp/adjacent

tan θ = opposite/adjacent cot θ = adjacent/opposite

find the trig values
Find the trig values

I

Find the indicated values:

1) sin G 2) sin I 3) cot G

9/41 40/41 40/9

4) cscG 5) cosI 6) sec H

41/9 9/41 Undef

41

G

H

40

building a right triangle
Building a Right Triangle
  • Descriptions always will tell you where the right angle is
  • Use the Pythagorean Theorem to find missing sides
  • Use arc trig functions to find missing angles

In ΔABC, C is the right angle. Find the remaining sides and angles. Round to the nearest tenth.

7) a = 5, b = 6

c= 7.8, A = 39.8˚, B = 50.2˚

8) a = 17, c = 22

b = 14.0, A = 50.6˚, B = 39.4˚

using triangles
Using Triangles
  • The bases on a baseball diamond form a square 90 ft on a side. The pitchers plate is 60 ft 6 in from the back corner of Home Plate.
  • How far is the pitcher’s plate from Second Base?

66 ft 9.6 in

  • How far is the pitcher’s plate form First Base?

63 ft 8.4 in

  • If a line drive is 10 ft high when it passes the Third Baseman 100 ft from Home Plate, at what angle did it leave the bat after making contact? (Assume the ball was hit at a height of 4 ft.)

θ ≈ 5.7˚

homework
Homework

For tomorrow:

Page 782 #2 – 24 even