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Trigonometric Ratios – Solving For Angles PowerPoint PPT Presentation


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Geometry A BowerPoint Presentation. Trigonometric Ratios – Solving For Angles. Calculator Practice. Try these on your calculator to make sure you are getting correct answers: Sin (0.7660444) = 50° Cos (0.4694716) = 62° Tan (3.73205081) = 75°

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Trigonometric Ratios – Solving For Angles

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Geometry a bowerpoint presentation

Geometry

A BowerPoint Presentation

Trigonometric Ratios – Solving For Angles


Calculator practice

Calculator Practice

  • Try these on your calculator to make sure you are getting correct answers:

    • Sin (0.7660444) = 50°

    • Cos (0.4694716) = 62°

    • Tan (3.73205081) = 75°

  • You may need to use a “2nd” function on your calculator to use sin x , cos x , tan x. Look above the buttons for sin x , cos x , and tan x.

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Solving for angles of right s

Solving for angles of right ∆s

  • If you know the lengths of any two sides of a right triangle, that is enough information to find the acute angles.

18

40


Step 1 choose an acute

Step 1 – Choose an acute ∡

  • We will solve for the angle that is x°

18

40


Step 2 label the sides

Step 2 – Label the sides

  • The hypotenuse is across from the right angle

  • Label the legs as opposite and adjacent (positions relative to the angle with x°)

18

40


Step 2 label the sides1

Step 2 – Label the sides

  • The hypotenuse is across from the right angle

  • Label the legs as opposite and adjacent (positions relative to the angle with x°)

hyp

18

opp

40

adj


Step 3 select ratio

Step 3 – Select ratio

  • Look at the two sides for which you know the lengths

  • We know opp = 18 and adj = 40

hyp

18

opp

40

adj


Step 3 select ratio1

Step 3 – Select ratio

  • Look at the two sides for which you know the lengths

  • We know opp = 18 and adj = 40

  • Which ratio has opp and adj?

hyp

18

opp

40

adj


Step 3 select ratio2

Step 3 – Select ratio

  • Look at the two sides for which you know the lengths

  • We know opp = 18 and adj = 40

  • Which ratio has opp and adj? SOH – CAH – TOA

TANGENT

hyp

18

opp

40

adj


Step 4 fill in and solve

Step 4 – Fill in and solve

opp

18

40

adj

tan x ° = = = 0.4500

hyp

18

opp

40

adj


Step 4 fill in and solve1

Step 4 – Fill in and solve

opp

18

40

adj

tan x ° = = = 0.4500

tan x ° = 0.4500 We will use the tan x buttonon a calculator to answer the question “What angle has a tangent of 0.4500?”

-1

hyp

18

opp

40

adj


Step 4 fill in and solve2

Step 4 – Fill in and solve

tan x ° = 0.4500 can be rewritten as

tan (0.4500) = x (You don’t have to rewrite it this way as long as you know what to do on your calculator)

-1

hyp

18

opp

40

adj


Step 4 fill in and solve3

Step 4 – Fill in and solve

tan x ° = 0.4500 can be rewritten as

tan (0.4500) = x

-1

x = 24.2

(rounded to nearest tenth)

hyp

18

opp

40

adj


Solving for angles of right

Solving for angles of right ∆

  • Step 1

    • Choose an acute angle

  • Step 2

    • Label sides of the triangle (hyp, opp, adj)

  • Step 3

    • Select ratio (sin, cos, tan)

  • Step 4

    • Fill in and solve


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