Answer: 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
