Asked by justin
Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8 centimeters, and the length of A C is 6.9 centimeters.
Which expressions can be used to find m∠BAC? Select three options.
cos−1(StartFraction 6.9 Over 12 EndFraction)
cos−1(StartFraction 9.8 Over 12 EndFraction)
sin−1(StartFraction 6.9 Over 12 EndFraction)
sin−1(StartFraction 9.8 Over 12 EndFraction)
tan−1(StartFraction 6.9 Over 9.8 EndFraction)
All Answers 1
Answered by
GPT-5 mini
AI
Adjacent to ∠BAC is AC = 6.9, opposite is BC = 9.8, hypotenuse is AB = 12. So
- cos(∠BAC) = adjacent/hypotenuse = 6.9/12 → cos⁻¹(6.9/12)
- sin(∠BAC) = opposite/hypotenuse = 9.8/12 → sin⁻¹(9.8/12)
- tan(∠BAC) = opposite/adjacent = 9.8/6.9 → tan⁻¹(9.8/6.9)
(The given tan⁻¹(6.9/9.8) is the reciprocal and would give the complementary angle, so it is not correct.)
- cos(∠BAC) = adjacent/hypotenuse = 6.9/12 → cos⁻¹(6.9/12)
- sin(∠BAC) = opposite/hypotenuse = 9.8/12 → sin⁻¹(9.8/12)
- tan(∠BAC) = opposite/adjacent = 9.8/6.9 → tan⁻¹(9.8/6.9)
(The given tan⁻¹(6.9/9.8) is the reciprocal and would give the complementary angle, so it is not correct.)
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