which equation can be used to find the measure of angle bac?\n○ tan⁻¹(5/12)=x\n○ tan⁻¹(12/5)=x\n○…

which equation can be used to find the measure of angle bac?\n○ tan⁻¹(5/12)=x\n○ tan⁻¹(12/5)=x\n○ cos⁻¹(12/13)=x\n○ cos⁻¹(13/12)=x

which equation can be used to find the measure of angle bac?\n○ tan⁻¹(5/12)=x\n○ tan⁻¹(12/5)=x\n○ cos⁻¹(12/13)=x\n○ cos⁻¹(13/12)=x

Answer

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$ for an acute angle $\theta$. For $\angle BAC$, the opposite side to $\angle BAC$ is $BC = 12$, the adjacent side is $AC = 5$, and the hypotenuse is $AB=13$.

Step2: Analyze tangent formula

$\tan\angle BAC=\frac{BC}{AC}=\frac{12}{5}$, so $\angle BAC=\tan^{- 1}(\frac{12}{5})$.

Step3: Analyze cosine formula

$\cos\angle BAC=\frac{AC}{AB}=\frac{5}{13}$, so $\angle BAC=\cos^{-1}(\frac{5}{13})$.

Answer:

$\tan^{-1}(\frac{12}{5}) = x$