Given:
The triangle ABC is a right angled triangle.
The length of AB is 10 m
The length of BC is a.
The measure of angle A is 38°
We need to determine the value of a.
Value of a:
The value of a can be determined using the formula,
[tex]sin \ \theta=\frac{opp}{hyp}[/tex]
where [tex]\theta=38^{\circ}[/tex], [tex]opp=BC[/tex] and [tex]hyp=AB[/tex]
Substituting these values, we get;
[tex]sin \ 38^{\circ}=\frac{BC}{AB}[/tex]
Substituting BC = a and AB = 10, we get;
[tex]sin \ 38^{\circ}=\frac{a}{10}[/tex]
Multiplying both sides of the equation by 10, we get;
[tex]sin \ 38^{\circ} \times 10=a[/tex]
[tex]0.6157 \times 10=a[/tex]
[tex]6.157=a[/tex]
Thus, the value of a is 6.157 m
