Objectives:
1. To win $1000 for
yourself
2. To win $500 for your
teacher
Assignment:
• Practice TRIG*STAR
problems
TRIG*STAR is a test
put together by the
National Society of
Professional
Surveyors (NSPS) to
find a trig star.
(The first trig star)
The test has just 4 questions, each of which is
broken up into multiple parts worth a total of
100 points.
• The first 3 questions are always the same with
different numbers. These are worth 70 points.
• The other 30 points come from a daunting
application question.
• Okay, so this one isn’t worth any points, but
it’s pretty important that you answer this
“question” correctly.
1. On a right triangle, you’re given two sides. You have
to find the other side and one of the angles.
Pythagorean
Theorem
Inverse
Trig
Important information!
  cos1  a / c 
b  c2  a2
If you don’t want to worry about rounding your
answers to the nearest hundredth, just set
your calculator MODE to 2 decimal places!
• Don’t worry, your calculator still knows all the
digits of a number if you store it; it’s just that
you’ll only see the two decimals.
2. On an obtuse triangle, you’re given two angles and the
included side. You have to find the third angle and all other
segments.
Triangle
Sum
Trig
Store as E
Store as G
Store as H
As far as work goes with the trig equations, only
write down what you need to in order to see if
you need to multiply by the denominator or
switch the denominator with the trig ratio.
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
1. Find m<BCD:
A
180 – m<BAD.
Store as C.
2. Draw in the other
diagonal.
3. Find the length of
new diagonal using
Law of Cosines.
Store as A.
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
4. Find <B (top part of
D
B
A
<CBA) using Law of
Sines. You’ll need
C, A, and side DC.
Store as B.
5. Find <D (bottom
part of <CBA):
90 – B. Store as D.
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
6. Find side AD using
D
B
A
F
E
Law of Sines. You’ll
need D, A, and
m<BAD. Store as E.
7. Find AC using the
Pythagorean
Theorem with E
and side DC. Store
as F.
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
8. Finally, find AB
D
B
A
F
E
using the
Pythagorean
Theorem with F
and side BC.
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
1. Store m<BAD as A.
y
x
A
A–x
2. Label <BAC as x
and <CAD as A – x.
3. Label diagonal AC
as y.
4. Set up a system of
equations to find x
and y.
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
sin x  504.27
y
sin  A  x   265.56
y
y
x
A
(Solve for y)
504.27
sin x
y
y  sin265.56
 A x 
A–x
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
6. Graph system of
equations to find
point of
intersection.
y
x
A
y  504.27
sin x
y  sin265.56
 A x 
A–x
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
6. Graph system of
equations to find
point of
intersection.
y
x
A
A–x
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
6. Graph system of
equations to find
point of
intersection.
y
x
A
A–x
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
7. Record the value of
y as AC. The values
of x and y are
stored as X and Y.
y
x
A
A–x
3. On a quadrilateral, you’re given two consecutive sides and
the opposite angle. You have to find the other two sides and
the diagonal.
8. Solve for AB using
P-Thag or
SohCahToa.
y
x
A
A–x
On the third question, label the diagram to match the one below.
Then solve a system of equations of this form:
y
y
x
A
A–x
Top
sin x
Right Side
y
sin  A  x 
Solve the system of equations by using a difference formula.
y  504.27
sin x
y  sin265.56
 A x 
Solve using the CT-Method.
Correctly answering those first three problems
will guarantee you 70 points. Remember,
those questions will always be the same;
they’ll just change the numbers.
The other 30 points comes from the last
question, which is a surveying application
problem drawn up in AutoCAD. This question
is the wildcard, and it’s always different.
4. On a surveying application, you’re given various angles and
lengths. You’ll have to find other sides and angles.
Don’t be afraid to add extra segments to your
drawing, especially on the last application
problem. Usually the segments given in the
picture are misleading, and you can’t solve the
problem with those alone.
*ADD SEGMENTS TO CREATE TRIANGLES!
Objectives:
1. To win $1000 for
yourself
2. To win $500 for your
teacher
Assignment:
• Practice TRIG*STAR
problems