The equation [tex]x=tan^{-1}(\frac{12}{5})[/tex] can be used to find the measure of ∠BAC ⇒ 2nd answer
Step-by-step explanation:
Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle
The trigonometry ratios of the ∠BAC, the opposite side to this angle is BC and the adjacent side to it is AB are
- [tex]sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}[/tex]
- [tex]cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}[/tex]
- [tex]tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}[/tex]
In Δ ABC
∵ ∠ BCA is a right angle
∴ The hypotenuse is AB
∵ The adjacent side to ∠CAB is AC
∵ The opposite side to ∠CAB is BC
∵ AB = 13 units ⇒ hypotenuse
∵ CB = 12 units ⇒ opposite
∵ AC = 5 units ⇒ adjacent
- Let us find the trigonometry ratios of angle BAC
∵ m∠CAB is x
∵ [tex]sin(x)=\frac{BC}{AB}[/tex]
∴ [tex]sin(x)=\frac{12}{13}[/tex]
∴ [tex]x=sin^{-1}(\frac{12}{13})[/tex]
∵ [tex]cos(x)=\frac{AC}{AB}[/tex]
∴ [tex]cos(x)=\frac{5}{13}[/tex]
∴ [tex]x=cos^{-1}(\frac{5}{13})[/tex]
∵ [tex]tan(x)=\frac{BC}{AC}[/tex]
∴ [tex]tan(x)=\frac{12}{5}[/tex]
∴ [tex]x=tan^{-1}(\frac{12}{5})[/tex]
The equation [tex]x=tan^{-1}(\frac{12}{5})[/tex] can be used to find the measure of ∠BAC
Learn more:
You can learn more about the trigonometry ratios in brainly.com/question/4924817
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