Answer:
x = 7.41 (nearest hundredth)
y = 9.53 (nearest hundredth)
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
From inspection of the triangle:
- [tex]\theta[/tex] = 39°
- O = 6
- A = x
- H = y
To find x, use the tan trigonometric ratio:
[tex]\implies \tan 39^{\circ}=\dfrac{6}{x}[/tex]
[tex]\implies x=\dfrac{6}{\tan 39^{\circ}}[/tex]
[tex]\implies x=7.409382939...[/tex]
Therefore, x = 7.41 (nearest hundredth)
To find y, use the sin trigonometric ratio:
[tex]\implies \sin 39^{\circ}=\dfrac{6}{y}[/tex]
[tex]\implies y=\dfrac{6}{\sin39^{\circ}}[/tex]
[tex]\implies y=9.534094374...[/tex]
Therefore, y = 9.53 (nearest hundredth)
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