Right Triangle Geometry and Trigonometric Ratios
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Questions and Answers

What is the relationship between the sides of the right triangle and angle θ?

  • Angle θ is opposite side t.
  • Angle θ is opposite side s. (correct)
  • Angle θ is the right angle.
  • Angle θ is adjacent to side t.

    • Which trigonometric function can be used to find angle θ given sides s and t?

  • sin(θ) = t/s
  • sin(θ) = s/t
  • cos(θ) = t/s
  • tan(θ) = s/t (correct)

    • If side s measures 7 cm and side t measures 9 cm, how would you calculate the value of angle θ?

  • Using arc sin of 9/7.
  • Using arc tan of 7/9.
  • Using arc cos of 7/9.
  • Using arc tan of 9/7. (correct)

    • Which of the following measures of angle θ is closest to the actual value?

    <p>56°</p> Signup and view all the answers

    What is the approximate decimal representation of angle θ's measurement in radians?

    <p>0.78 radians</p> Signup and view all the answers

    Study Notes

    Right Triangle Geometry

    • The problem involves a right triangle with two known sides: side s (7 cm) and side t (9 cm).
    • The angle θ is the unknown angle.
    • To find the measure of angle θ, we need to use trigonometric ratios.

    Trigonometric Ratios

    • SOH CAH TOA is a mnemonic used to remember the trigonometric ratios:
      • SOH: Sine = Opposite / Hypotenuse
      • CAH: Cosine = Adjacent / Hypotenuse
      • TOA: Tangent = Opposite / Adjacent

    Solving for Angle θ

    • In this triangle:
      • Side s is opposite angle θ.
      • Side t is adjacent to angle θ.
    • We can use the tangent ratio (TOA):
      • tan θ = Opposite / Adjacent = s / t
      • tan θ = 7 / 9
    • To find θ, we need to use the inverse tangent function (arctan or tan⁻¹):
      • θ = arctan (7/9)
    • Using a calculator, we get:
      • θ ≈ 37.87°

    Answer

    • None of the provided answer choices (A. 56°, B. 51°, C. 34°, D. 39°) are the correct answer.
    • The correct answer is approximately 37.87°.

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    Description

    This quiz focuses on the geometry of right triangles, specifically using trigonometric ratios to find an unknown angle. Participants will apply the SOH CAH TOA mnemonic to calculate angle θ using the tangent function. Challenge your understanding of trigonometry in right triangles!

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