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.

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:

`\\ (a)/(sinA) = (b)/(sinB) = (c)/(sinC)`

We know that sin(90º) = 1.

`\\ (a)/(sin(48.31)) = (b)/(sin(41.69)) = (49.9)/(1)`

Then, a is:

`\\ (a)/(sin(48.31)) = (49.9)/(1)`

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

`\\ a = 49.9*0.7467`

`\\ a = 37.26`

Thus, b is:

`\\ (b)/(sin(41.69)) = (49.9)/(1)`

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

`\\ b = 33.12`