Use the right triangle and the given information to solve the triangle. a=5 B=53degrees find b c and A

A = 37°

c = 8.31

b = 6.63

Step-by-step explanation:

I suppose that the triangle is something like the one below.

Then we know the measure of an angle and the length of the adjacent cathetus.

a = 5

B = 53°

Now we can use the relationships:

Tan(B) = (opposite cathetus)/(Adjacent cathetus) = b/a

Cos(B) = (adjacent cathetus)/(hypotenuse) = a/c

Sin(B) = (opposite cathetus)/(hypotenuse) = b/c

Then we have:

Tan(53°) = b/5

Tan(53°)*5 = b = 6.63

So we found the length of b.

Now we can use the second relationship to find the length of c:

cos(53°) = 5/c

c = 5/cos(53°) = 8.31

Now, to find the angle A we can use the fact that the sum of all interior angles of a triangle must be equal to 180°

We know that is a triangle rectangle, so we have an angle equal to 90°, this one is C = 90°, and we also know that B = 53°

Then:

A + B + C = 180°

A + 53° + 90° = 180°

A + 53° = 180° - 90° = 90°

A = 90° - 53° = 37°

Then:

A = 37°

c = 8.31

b = 6.63