PART I lesson, inquiry mode

1) Consider a right angle. The right angle is A and the hypotenuse is a. The other legs are b (opposite angle B) and c (opposite angle is B). draw the triangle below and right the pythagorian theorem:


2) If the triangle is not right, but if we keep the same configuration (leg a across angle A, leg b across angle B, leg c across angle C) the formula becomes:

 a² = ___________________   it is called the law of cosines. Note the connection a and A.

Not that if A = 90 degrees then a² = ___________. This is the ____________ theorem.

Write the law for leg c,  c² = ____________________ then for leg b,  b² = ______________

Use the law of cosines when solving for a triangle if  you have 1 angle and 2 legs.
If you are given 2 angles and 1 leg, use the law of sines that you will derive below.
Also: sum of angles in a triangle = 180. REmember that for now. (use an index card)

3) Using the law,  you can also solve for the angle.
cosA = _________________ (in terms of a, b and c)

4) problem: a = 8ft, b =19ft, c =14ft. Solve the triangle.
Find the size of the angles A, B and C
cosA = ________________ = __________ so A  = ___________

cosB= _________________= __________ so B = ____________

Because A + B + C = 180, then C = ______

5)  Suppose we want to solve a triangle, given the information:
A = 55 degrees, b =3, c = 10
first solve for a . a² = _________________ so a = _________
Then solve for the angle B
cosB= ________________ so B = _____________
Since A + B + C = 180, then C = _________

6) Consider the triangle below:


Can you show that sinA/a = sinB/B

hint: In the right triangle (H1, H2, B), find sinB = __________

In the right triangle (A, H1, H2), find sinA= ____________

Then compare sinA/a to sinB/b

This is called the law of sinus.
You can use both laws to solve a triangle. sinA/a = sinB/b = sinC/c

PART II: Assignments from the book.
1) p.299 14,  18, 6, 8

2) p. 301 # 34A)

The
p.388
hint: - call the origin 0 - Find OP1, using 25 degrees (soh cah toa)
- Find OP2 using 50 degrees. Work with the triangle OP1P2 - use the law of cosine

3) # 30
hint: solve for leg a (law of sine) - solve for leg b -

4) # 31
hint:

first work in the blue triangle and solve for the leg x (law of sines since you know 2 angle)
Then work in the right angle triangle to solve for h

5) # 34do the bridge one
hint; first the law of sines (you have 2 angles, then the law of cosines)

6) # 36
trace the radius. Work in both triangles formed.

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