Inclination of path

s_ingram · #1 $Old$ November 3rd, 2009, 04:58 AM

Hi guys!
I am getting the wrong answer for the following question: a diagram is attached.
A hillside forms a plane surface inclined at $25 \deg$ to the hoizontal. A straight path up the hillside makes an angle of $60 \deg$ 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 $\triangle ORS.$
tan 25 = h / OS
OS = h / tan 25
from $\triangle OQS.$
cos 60 = OS/OQ
OQ = OS / cos 60.
OQ = h /(tan 25. cos 60)
from $\triangle OPQ. \tan \alpha = h / OQ = tan25. cos 60$
$\alpha = tan^-1 (tan25. cos 60) = 13.1 \deg$
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?

aidan · #2 $Old$ November 3rd, 2009, 05:49 AM

My result is 13.1243 degrees.
You are correct.
The book has a typo.

s_ingram · #3 $Old$ November 3rd, 2009, 06:01 AM

I was hoping someone would say that!