Respuesta :
Assuming angle A is opposite to side a, B is the opposite to side b, and angle C is the opposite to side c.
Answer:
The right triangle has the following angles:
A = 48.31º, B = 41.69º and C = 90º.
The sides are:
[tex] \\ a = 37.26[/tex], [tex] \\ b = 33.12[/tex] and c = 49.9.
Step-by-step explanation:
The inner sum of a triangle = 180º.
A=48.31º,
C=90º
A + B + C = 180º
48.31º+ B + 90º = 180º
B = 180º - 90º - 48.31º
B = 41.69º
We can apply the Law of Sines to solve for unknown sides:
[tex] \\ \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]
We know that sin(90º) = 1.
[tex] \\ \frac{a}{sin(48.31)} = \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]
Then, a is:
[tex] \\ \frac{a}{sin(48.31)} = \frac{49.9}{1}[/tex]
[tex] \\ a = 49.9*sin(48.31)[/tex]
[tex] \\ a = 49.9*0.7467[/tex]
[tex] \\ a = 37.26[/tex]
Thus, b is:
[tex] \\ \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]
[tex] \\ b = 49.9*sin(41.69)[/tex]
[tex] \\ b = 33.12[/tex]
