This activity is intended to supplement Trigonometry, Chapter 5, Lesson 2.
Problem 1 - Consider a 3, 4, 5 right triangle.
- Draw the triangle.
- Find the area using A=12bh.
- Consider Heron’s Formula, A=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√
In Y=, plug into Y1=x(x−3)(x−4)(x−5)−−−−−−−−−−−−−−−−−−√. Zoom in by changing the window. Press WINDOW and change the parameters to the right.
- Describe the graph. Does it have any x or y intercepts?
- In Y2, type Y2=12⋅3⋅4 or 6, the area of this triangle. Press GRAPH. Do the two functions intersect? If so, write the point(s) below.
Y1 is Heron’s formula with a=3, b=4, and c=5 and s=x. What do the point(s) above tell us about this specific Heron’s formula? What do (x, y) represent?
Repeat the steps from Problem 1 with the triangle below.
Are your findings the same?