The best approximation for the measure of angle XYZ is 39.8° ⇒ 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 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 XYZ
∵ ∠ YXZ is a right angle
∴ The hypotenuse is YZ
∵ The adjacent side to ∠XYZ is XY
∵ The opposite side to ∠XYZ is XZ
∵ YX = 12 units
∵ XZ = 10 units
- Use tan ratio to find the measure of the angle because you
have the adjacent and opposite sides of the angle XYZ
∵ m∠XYZ is x
∵ [tex]tan(x)=\frac{XZ}{XY}[/tex]
∴ [tex]tan(x)=\frac{10}{12}[/tex]
- To find x use the inverse of tan(x)
∵ [tex]x=tan^{-1}(\frac{10}{12})[/tex]
∴ x = 39.8°
∴ m∠XYZ = 39.81°
The best approximation for the measure of angle XYZ is 39.8°
Learn more:
You can learn more about the trigonometry ratios in brainly.com/question/4924817
#LearnwithBrainly
