Mathematics: Which expressions can be used to find m∠bac? check all that apply. cos−1 cos−1 sin−1 sin−1 tan−1 tan−1

Which expressions can be used to find m∠bac? check

Ответ:

justnbri

16.01.2022

Mathematics

A, D, F

Step-by-step explanation:

Angle BAC is angle A in triangle ABC. Use the definitions of the trigonometric functions:

$\cos \angle A=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{AC}{AB}=\dfrac{6.9}{12}\\ \\\sin \angle A=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}=\dfrac{9.8}{12}\\ \\\tan \angle A=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{BC}{AC}=\dfrac{9.8}{6.9}\\ \\\cot \angle A=\dfrac{\text{adjacent leg}}{\text{opposite leg}}=\dfrac{AC}{BC}=\dfrac{6.9}{9.8}$

Now

$\angle A=\cos^{-1}\left(\dfrac{6.9}{12}\right)\\ \\\angle A=\sin^{-1}\left(\dfrac{9.8}{12}\right)\\ \\\angle A=\tan^{-1}\left(\dfrac{9.8}{6.9}\right)\\ \\\angle A=\cot^{-1}\left(\dfrac{6.9}{9.8}\right)$

So, correct options are A, D and F

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Which expressions can be used to find m∠bac? check all that apply. cos−1 cos−1 sin−1 sin−1 tan−1 tan−1

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