an example problem showed the following

log tan A/2 = 9.54435 - 10
A= 38 deg 36' 12"

Now i want to do the same.

log tan A/2 = 9.85551 - 10
A= ??

I don't know how to convert tan into degrees can you help me.

log tan A/2 = 9.85551 - 10

log tan A/2 = - 0.14449
take inverse log
tan A/2 = 0.716984884
take inverse tangent
A/2 = 35.64
A = 71.28°
= 71° 16' 48"

To solve for A in the equation log tan(A/2) = 9.85551 - 10, you need to first isolate the term tan(A/2). To do this, you need to remove the logarithm by taking the inverse logarithm (exponentiation). In this case, since the logarithm is base 10, you need to raise 10 to the power of the expression on the right side of the equation.

So, step by step, you can follow these instructions:

1. Add 10 to both sides of the equation to get:
log tan(A/2) + 10 = 9.85551

2. Raise 10 to the power of both sides of the equation to remove the logarithm, resulting in:
10^(log tan(A/2) + 10) = 10^(9.85551)

3. Simplify the right side of the equation, which gives:
tan(A/2) * 10 = 10^(9.85551)

4. Divide both sides of the equation by 10 to solve for tan(A/2):
tan(A/2) = 10^(9.85551) / 10

Now, to convert the tangent value into degrees, you need to use the inverse tangent function (also known as arctangent or atan). This function will give you the angle whose tangent matches the given value.

5. Use the inverse tangent function to find A/2:
A/2 = atan(tan(A/2))

6. Multiply A/2 by 2 to find A:
A = 2 * atan(tan(A/2))

Finally, substitute the value of tan(A/2) obtained in step 4 into the equation from step 6 to calculate the value of A.