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Questions and Answers
What is the relationship between the sides of the right triangle and angle θ?
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?
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?
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?
Which of the following measures of angle θ is closest to the actual value?
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What is the approximate decimal representation of angle θ's measurement in radians?
What is the approximate decimal representation of angle θ's measurement in radians?
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Study Notes
Right Triangle Geometry
- The problem involves a right triangle with two known sides: side
s(7 cm) and sidet(9 cm). - The angle
θis 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
sis opposite angleθ. - Side
tis adjacent to angleθ.
- Side
- 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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