Calculating the slope of a frog's head (C) Daniel Friedman Frog Measurements: frog's head slope in degrees
How can we measure the slope of a frog's head or anything else?
How to measure dimensions of an animal or an object from a distance

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Frog data measurements:

How might we determine the slope of a frog's head from nose tip to eye-top? Here we describe measurements that let us calculate the frog's head slope in degrees and we cite an alternative method using a folding ruler that could have been used to get frog (or other animal) dimensions from a distance - which sometimes is a better idea. .

This article series gives clear examples just about every possible way to figure out any or all roof, stair, or other building slopes & construction dimensions and measurements expressing the area, width, length, slope, rise, run, and unit rise in inches per foot.

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All of the Ways to Get the Slope of a Frog, a Roof or the angle anything else that is sloping

Calculating the slope of a frog's head (C) Daniel Friedman

With just a small amount of effort one could calculate the slope of anything, even a frog's head. We measured this frog's head last spring. The frog was too nervous to allow use of my angle-finder level so I took a different approach. I made some rough measurements of his little head.

[Click any image to see an enlarged, detailed version]

Dimension (a) from the frog's nose to the top of his eye was 0.75 inches.

Dimension (b) from the frog's nose to directly under the top of his eye turned out to be 0.63inches.

Dimension (c) - the green line happened to be 0.5 - about a half of an inch.

At this point the frog left before I could get out my angle measuring protractor. But the tangent function came to the rescue.

Using Tangents to Study Frogs

Right triangle side lengths relationship  - InspectApedia

Tangent (Frogs head slope) = (Frog Nose Rise / Frog Jaw Length)

or for the particular frog under examination,

Tangent (Frogs head slope) = (c) / (b) = 0.5 / 0.63 inches = .873

I used Tan-1 (0.873) to convert the tangent to slope in degrees = 41 degrees - which looks about right, right?

This frog's head slopes from nose to eye top at 41 deg.

Student Exercise: Measure the Angle of This Frog's Face

Frog in a pond in Laurentides in Quebec, Canada (C) Daniel Friedman

The handsome frog shown above posed on water lillies in a pond in the Laurentides region of Quebec while I was at spore camp. The darker green triangle on the top of the frog's head from tip of nose to those round (ovate) ears would be another easy-to-spot triangle whose angle you can measure using the method we've given above.

A neat trick that we could have used to measure the angle of the frog's head without ever getting close to it is shown using a folding ruler explained

You can calculate slope of anything, even a frog if you know just one or two measurements.

Details are in the articles listed just below.

You can estimate the roof slope from the ground by any of several methods described

A sickening amount of fun and explanation of messing with roof slopes, angles, rulers, and a protractor are demonstrated


Obviously there are other very precise ways to make measurements from a distance, as any surveyor knows, using geometry, trigonometry, and instruments such as a sextant, dumpy level, a theodolite, GPS devices, and more.

Building & Roof Measurement Articles


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