Answer:
y = 32.0°
Step-by-step explanation:
As the given triangle is a right triangle, use trigonometric ratios to solve.
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] = y
- O = 9 cm
- H = 17 cm
Therefore, use the sine trigonometric ratio to find y:
[tex]\implies \sin y = \dfrac{9}{17}[/tex]
[tex]\implies y=\sin^{-1} \left( \dfrac{9}{17} \right)[/tex]
[tex]\implies y = 31.96571875...^{\circ}[/tex]
[tex]\implies y=32.0\:\:\sf(nearest\:tenth)[/tex]
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