Answer:
x = 7.41 (nearest hundredth)
y = 9.53 (nearest hundredth)
Step-by-step explanation:
<u>Trigonometric ratios</u>
![\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}](https://tex.z-dn.net/?f=%5Csf%20%5Csin%28%5Ctheta%29%3D%5Cdfrac%7BO%7D%7BH%7D%5Cquad%5Ccos%28%5Ctheta%29%3D%5Cdfrac%7BA%7D%7BH%7D%5Cquad%5Ctan%28%5Ctheta%29%3D%5Cdfrac%7BO%7D%7BA%7D)
where:
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:
= 39°- O = 6
- A = x
- H = y
To find x, use the tan <u>trigonometric ratio</u>:
![\implies \tan 39^{\circ}=\dfrac{6}{x}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctan%2039%5E%7B%5Ccirc%7D%3D%5Cdfrac%7B6%7D%7Bx%7D)
![\implies x=\dfrac{6}{\tan 39^{\circ}}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D%5Cdfrac%7B6%7D%7B%5Ctan%2039%5E%7B%5Ccirc%7D%7D)
![\implies x=7.409382939...](https://tex.z-dn.net/?f=%5Cimplies%20x%3D7.409382939...)
Therefore, x = 7.41 (nearest hundredth)
To find y, use the <u>sin trigonometric ratio</u>:
![\implies \sin 39^{\circ}=\dfrac{6}{y}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csin%2039%5E%7B%5Ccirc%7D%3D%5Cdfrac%7B6%7D%7By%7D)
![\implies y=\dfrac{6}{\sin39^{\circ}}](https://tex.z-dn.net/?f=%5Cimplies%20y%3D%5Cdfrac%7B6%7D%7B%5Csin39%5E%7B%5Ccirc%7D%7D)
![\implies y=9.534094374...](https://tex.z-dn.net/?f=%5Cimplies%20y%3D9.534094374...)
Therefore, y = 9.53 (nearest hundredth)
Learn more about trigonometric ratios here:
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