Hamilton's Math To Build On - copyright 1993

Finding Degrees on Sloped Objects

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* Finding Degrees on Sloped Objects

Once you know how to calculate
measurements for angles and leg
lengths of right triangles, you can
use that same knowledge to find
the angle measurements for slopes.
One leg length can be determined by
holding a straightedge level to the slope
(this drawing shows the straightedge
placed horizontally) and measuring the
distance between the other end of the
straightedge and the slope. Since you
know the length of the straightedge, you
know the length of the other leg.

Once you have these measurements,
calculating the angle is a matter of using
the appropriate formula. Notice that no
matter which angle you choose to calculate
for, the known measurements are for the
adjacent or the opposite side; however,
which side is the adjacent side and which
side is the opposite side is dependent upon
which angle you are calculating for.

Because of this, always be mindful of which of the two angles you are calculating for when using this procedure. Since the length of the adjacent side and the opposite side are known, the tangent function is used to find the angle.

Note: For the straightedge, I usually use a framing square with a torpedo level or a four foot level. I find this more accurate than using mechanical angle finders.


* Isosceles Triangle

Knowing that a bisecting line divides an isosceles triangle into two equal right triangles helps when drawing an isosceles triangle.

First: From a horizontal line, draw a perpendicular line using a compass.

Second: Use your compass to mark equal line segments on both sides of the vertex of the 90° angles.

Third: Pick a point on the vertical line and draw lines from both endpoints of the line segments to the point on the vertical line.

Voilà, an isosceles triangle.

On to Drawing Circles

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18 September 1995
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