13y = 15x
tangent = y / x for an angle in the first quadrant, Q1.
The reference angle forms a right triangle with a base of x and a height of y.
From the equation 13y = 15x y = 15x / 13 y/x = 15/13 tan (theta) = 15/13
Find the Arctan (15/13), which = tan^(-1) (15/13) = 49 degrees to two significant digits
49 degrees * ( pi radians / 180 degrees ) = 0.86 radians to two significant digits
20.0185 expressed with 3 significant figures does not always mean to round to 3 figures.
Here is a good reference link http://www.usca.edu/chemistry/genchem/sigfig.htm
All non-zero digits are significant. All zeroes between two significant digits are significant. Zeroes not followed by a significant digit are not significant.
20.0185 has two zeroes and both are significant because they are between the 2 and the 1.
The 2 is significant because it is non-zero. Count the FIRST three significant digits from the left to the right. Do NOT round up or down.
This results in: 20.0
My son just learned this in this school year (11th grade).
Current educators in secondary mathematics teach students to use a method called "synthetic division."
However, following the same steps used for long division of whole numbers, a student can easily learn how to do "long division" in algebra, which includes variables, coefficients, and whole numbers.
Either can be searched online. Many students like synthetic division. I just think it is one extra technique to memorize when students already are proficient in long division of whole numbers.
Using your algebra skills stepwise:
(x/100)*(1/3) = (5/9)
(x/100) = (5/9)*(3/1)
(x/100) = 15/9
x = (15/9)*100
x = 1500/9 = 500/3 = 16.6666
x = 16.67 % as a percent to two decimal places
* Note: The use of 100 in the algebra was not entirely necessary, but using 100 often helps students with problems using percent notation.
Look up a trig. identity for cos (a + b) by searching for "trigonometric identities.'
Then use a = 90 degrees and b = -10 degrees.
cos 90 degrees = zero, so the expression is just equal to the cos(-10 degrees).
How you should answer this problem depends on what references the you are allowed to use.
"Old school" trigonometry books had tables for all the trig function values of each individual degree.
I have such a book. I could give you the answer to four decimal places and the reference for the book.
Because of this, you might search for a "Trigonometry Table."
Provide me with the references you are allowed to use, and I will search for links to help you find a solution.