Respuesta :
The value of b is 5.4
Explanation:
Given that ABC is a triangle.
It is also given that [tex]a=12[/tex] , [tex]\angle B=25^{\circ}[/tex] and [tex]\angle C=45^{\circ[/tex]
We need to find the value of b.
The value of b can be determined using the law of sine formula, which is given by
[tex]\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sin C}[/tex]
First, we shall find the angle of A.
Since, ABC is a triangle and all the angles in a triangle add up to 180°
Thus, we have,
[tex]\angle A+\angle B+\angle C=180[/tex]
[tex]\angle A+25+45=180[/tex]
[tex]\angle A+70=180[/tex]
[tex]\angle A=110^{\circ}[/tex]
Thus, the value of angle A is 110°
Let us substitute these values in the law of sine formula.
Hence, we get,
[tex]\frac{12}{sin \ 110^{\circ}} =\frac{b}{sin \ 25^{\circ}}[/tex]
Simplifying, we get,
[tex]\frac{12}{0.9397} =\frac{b}{0.423}[/tex]
Multiplying both sides of the equation by 0.423, we get,
[tex]\frac{12\times 0.423}{0.9397} =b[/tex]
Simplifying, we get,
[tex]\frac{0.5076}{0.9397} =b[/tex]
Dividing, we have,
[tex]5.4=b[/tex]
Thus, the value of b is 5.4
