the point B is its vertex. If no other angle with
vertex at B is under consideration, 
may be shortened to just 
Triangle ABC is denoted by 
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2. Angles and Triangles
The angle formed by segments BA and BC (or rays BA
and BC) is denoted by
the point B is its vertex. If no other angle with
vertex at B is under consideration,
may be shortened to just
Triangle ABC is denoted by
Figure 3a |
Figure 3b |
The sum of the lengths of two sides of a triangle is
always greater than the length of the third side. For example, a
+ b > c in Figures 3a and 3b. Angles are measured either
in degrees or radians. The degree measure of a right angle is 90o
and its radian measure is 
The sum of the degree measures of the angles of a triangle is 180o
and the sum of their radian measures is 
An angle of a triangle is acute, right, or
obtuse
depending on whether its degree measure is respectively, less than, equal
to, or greater than 90o. The notation 
means that the degree measure of 
is 30o and 
means that the radian measure of
is 
A triangle with one 90o angle is called
a right triangle. The side opposite the right angle is called the hypotenuse.
In Figure 3b, 
and side c is the hypotenuse. The famous Theorem of Pythagoras states
that a triangle is a right triangle if and only if the square of the length
of one side equals the sum of the squares of the lengths of the other two
sides. (For example, c2 = a2 + b2
in Figure 3b.) The main steps of a proof follow:
Let 
have a right angle at C. Place a square of side c externally
on the hypothenuse
AB. Then place copies of
on the other three sides of the square. See Figure 4. All together, we
now have a big square whose sides have length a + b.
Now we get
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Figure 4 |
When laying out the foundation of a new building, stakes are driven
at the four corners. Measuring the proper distances between the stakes
is relatively easy, but measuring the angles properly is much more difficult.
After driving the stakes, the builder always measures the diagonal distance
to make sure it satisfies the Theorem of Pythagoras thereby insuring that
the angles are 90o. Suppose that the points A, B, and
C
in Figure 3b are three of the four corner stakes of a rectangular foundation,
a
= 36 ft, and b = 40 ft. What must c be to insure 
Give your answer to the nearest 10th of an inch.
Solution: We will assume the calculator has already been set
to Fix 1 display mode (see
Preface). We will let the calculator keep track of the units for us,
so the first sequence is to get to the appropriate units menu: RS UNITS
m-LENGTH. For each of the given lengths we will enter the value, attach
the units, then square it: 36 m-FT LS x2 40 m-FT LS x2.
We now have the squares of a and b on the stack. To find
c
we must add these, take the square root, then convert the result to inches:
+ 
LS m-IN.
We see the answer 645.8_in on the display. For complete instructions on
the use of units see Chapter 10 of UG.
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