Respuesta :
Option a: [tex]17.32 \ {m}[/tex] is the length of b
Explanation:
The angle of B is [tex]\angle B=60^{\circ}[/tex] and [tex]a=10 \ m[/tex]
We need to determine the length of b.
First, let us determine the angle of A.
Since, ABC is a triangle, then all the angles add up to 180°
Thus, we have,
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]\angle A+60^{\circ}+90^{\circ}=180^{\circ}[/tex]
[tex]\angle A+150^{\circ}=180^{\circ}[/tex]
[tex]\angle A=30^{\circ}[/tex]
Thus, the angle of A is [tex]\angle A=30^{\circ}[/tex]
Now, we shall determine the length of b using the sine law formula.
The formula for sine law is given by,
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}[/tex]
where [tex]a=10 \ m[/tex] , [tex]\angle A=30^{\circ}[/tex] , [tex]\angle B=60^{\circ}[/tex]
Thus, we have,
[tex]\frac{10}{\sin 30}=\frac{b}{\sin 60}[/tex]
Simplifying, we get,
[tex]\frac{10}{0.5}=\frac{b}{0.866}[/tex]
Multiplying both sides by 0.866, we get,
[tex]\frac{10\times0.866}{0.5}=b[/tex]
Multiplying the numerator, we have,
[tex]\frac{8.66}{0.5}=b[/tex]
Dividing, we get,
[tex]17.32=b[/tex]
Thus, the length of b is [tex]b=17.32 \ m[/tex]
Hence, Option a is the correct answer.
