The best approximation for the measure of angle ABC is 58.3° ⇒ 3rd 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 angle 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 ∠ABC is BC
∵ AB = 20 centimeters
∵ BC = 10.5 centimeters
- Use cosine ratio to find the measure of the angle because you
  have the adjacent side of the angle ABC and the hypotenuse
∵ m∠ABC is x
∵ [tex]cos(x)=\frac{BC}{AB}[/tex]
∴ [tex]cos(x)=\frac{10.5}{20}[/tex]
- To find x use the inverse of cos(x)
∵ [tex]x=cos^{-1}(\frac{10.5}{20})[/tex]
∴ x = 58.33°
∴ m∠ABC = 58.33°
The best approximation for the measure of angle ABC is 58.3°
Learn more:
You can learn more about the trigonometry ratios in brainly.com/question/4924817
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