Hi guys!

I am getting the wrong answer for the following question: a diagram is attached.

A hillside forms a plane surface inclined at $\displaystyle 25 \deg$ to the hoizontal. A straight path up the hillside makes an angle of $\displaystyle 60 \deg$ with the line of greatest slope. Find to the nearest degree, the inclination of the path to the horizontal.

I have: h = PQ = RS

from $\displaystyle \triangle ORS.$

tan 25 = h / OS

OS = h / tan 25

from $\displaystyle \triangle OQS.$

cos 60 = OS/OQ

OQ = OS / cos 60.

OQ = h /(tan 25. cos 60)

from $\displaystyle \triangle OPQ. \tan \alpha = h / OQ = tan25. cos 60$

$\displaystyle \alpha = tan^-1 (tan25. cos 60) = 13.1 \deg$

To the nearest degree this is 13.

The answer I have in my maths book is 12 degrees.

So, dear friends, am I wrong or is the book wrong?