NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Angular inclination of an interstate highway
From: Lu Abel
Date: 2013 Dec 31, 11:51 -0800
From: Lu Abel
Date: 2013 Dec 31, 11:51 -0800
A 7% grade means there is a 7 ft change in elevation for every 100 ft of horizontal travel. So what is being asked for is the arctangent of 7/100 or 0.07
Good rule-of-thumb people know that arcsin(X) = arctan(X) = X for small values of X. But those angles are in radians. (As Frank points out, angles are ratios, specifically of arc traversed vs radius; those angles are pure numbers (no measurement unit needed, unlike degrees or grads).
A radian is approximately 60 degrees (more closely, 57.3 degrees).
Using 60 degrees, 0.07 x 60 comes out to 4.2 degrees.
Good rule-of-thumb people know that arcsin(X) = arctan(X) = X for small values of X. But those angles are in radians. (As Frank points out, angles are ratios, specifically of arc traversed vs radius; those angles are pure numbers (no measurement unit needed, unlike degrees or grads).
A radian is approximately 60 degrees (more closely, 57.3 degrees).
Using 60 degrees, 0.07 x 60 comes out to 4.2 degrees.
From: Frank Reed <FrankReed@HistoricalAtlas.com>
To: luabel@ymail.com
Sent:
Subject: [NavList] Angular inclination of an interstate highway
Here's a road sign from Google Street View imagery in southern Texas. According to someone who posted a similar image on flickr, this is the steepest incline on I-10, which runs across the southern US from Florida to California.What is the angular inclination of this downhill slope in degrees (to the nearest tenth)? No calculator and no trig allowed. You can do it in your head with that magic number, 3438. Again: angles ARE ratios. We only quote them in degrees and minutes for historical continuity..After you've done the calculation in your head, consider the possible trig solutions. Are they any better?-FER
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