Answer:
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
Given:
- [tex]\theta[/tex] = 28°
- A = x
- H = 25
[tex]\implies \sf \cos(28^{\circ})=\dfrac{x}{25}[/tex]
[tex]\implies \sf x=25cos(28^{\circ})[/tex]
[tex]\implies \sf x=22.1\:(nearest\:tenth)[/tex]
Given:
- [tex]\theta[/tex] = 26°
- A = 15
- H = x
[tex]\implies \sf \cos(26^{\circ})=\dfrac{15}{x}[/tex]
[tex]\implies \sf x=\dfrac{15}{\cos(26^{\circ})}[/tex]
[tex]\implies \sf x=16.7\:(nearest\:tenth)[/tex]
Given:
- [tex]\theta[/tex] = 41°
- O = x
- A = 16
[tex]\implies \sf \tan(41^{\circ})=\dfrac{x}{16}[/tex]
[tex]\implies \sf x=16\tan(41^{\circ})[/tex]
[tex]\implies \sf x=13.9\:(nearest\:tenth)[/tex]
