Answer:
[tex]\sf a=\boxed{13}\:cm[/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
Given:
- [tex]\theta[/tex] = 31°
- O = a
- H = 25 m
[tex]\implies \sf \sin(31^{\circ})=\dfrac{a}{25}[/tex]
[tex]\implies \sf a=25\sin(31^{\circ})[/tex]
[tex]\implies \sf a=12.87595187...\:cm[/tex]
Therefore, a = 13 cm (to the nearest whole number)
