Question

Solve the right triangle.A = 48.31º. c = 49.9​

Answer 1

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:

$\\ a = 37.26$, $\\ b = 33.12$ 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:

$\\ \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

We know that sin(90º) = 1.

$\\ \frac{a}{sin(48.31)} = \frac{b}{sin(41.69)} = \frac{49.9}{1}$

Then, a is:

$\\ \frac{a}{sin(48.31)} = \frac{49.9}{1}$

$\\ a = 49.9*sin(48.31)$

$\\ a = 49.9*0.7467$

$\\ a = 37.26$

Thus, b is:

$\\ \frac{b}{sin(41.69)} = \frac{49.9}{1}$

$\\ b = 49.9*sin(41.69)$

$\\ b = 33.12$