Answer:
[tex]\sf x=8{\sqrt{2}[/tex]
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)
Therefore, to find x we need to use the sine trig ratio.
Given:
- [tex]\theta[/tex] = 45°
- O = x
- H = 16
Substitute these values into the formula and solve for x:
[tex]\implies \sf \sin(\theta)=\dfrac{O}{H}[/tex]
[tex]\implies \sf \sin(45^{\circ})=\dfrac{x}{16}[/tex]
[tex]\implies \sf x=16 \sin(45^{\circ})[/tex]
[tex]\implies \sf x=16 \cdot \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies \sf x=8{\sqrt{2}[/tex]
