Geometry 10-5a GeoGebra Primer: Triangle Area & The Law of Sines
By Matt Richardson
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Last updated about 3 years ago
7 Questions
Slide the Slide Me! slider in the applet below then begin the items that follow.
10 points
10
Question 1
1.
Exploration: Consider the yellow triangle on the left. Write an equation that expresses the relationship among ∠B, the triangle's height, and side c. Let h represent the triangle's height.
Exploration: Consider the yellow triangle on the left. Write an equation that expresses the relationship among ∠B, the triangle's height, and side c. Let h represent the triangle's height.
10 points
10
Question 2
2.
Exploration: Isolate h in the equation from the previous item. Enter the new equation. Note: h should be written in terms of c and B.
Exploration: Isolate h in the equation from the previous item. Enter the new equation.
Note: h should be written in terms of c and B.
10 points
10
Question 3
3.
Exploration: Now consider the pink right triangle on the right. Write an equation that expresses the relationship among ∠C, side b, and the triangle's height, h.
Exploration: Now consider the pink right triangle on the right. Write an equation that expresses the relationship among ∠C, side b, and the triangle's height, h.
10 points
10
Question 4
4.
Exploration: Isolate h in the equation from the previous item. Enter the new equation.Note: h should be written in terms of b and C.
Exploration: Isolate h in the equation from the previous item. Enter the new equation.
Note: h should be written in terms of b and C.
10 points
10
Question 5
5.
Exploration: Take your responses to items (2) and (4) to write a new equation that expresses the relationship among C, B, c, and b. Write this equation so that C and c appear on one side of the equation and that B and b appear on the other.
Exploration: Take your responses to items (2) and (4) to write a new equation that expresses the relationship among C, B, c, and b. Write this equation so that C and c appear on one side of the equation and that B and b appear on the other.
The same applet from above is embedded again for your convenience.
10 points
10
Question 6
6.
Exploration: Now drag the slider in the upper right hand corner. Given the fact that the length of segment BC would be denoted as a (it's just not drawn in the applet above), write an expression for the area of this original pink triangle, △ABC, in terms of a, b, and C.
Exploration: Now drag the slider in the upper right hand corner. Given the fact that the length of segment BC would be denoted as a (it's just not drawn in the applet above), write an expression for the area of this original pink triangle, △ABC, in terms of a, b, and C.
10 points
10
Question 7
7.
Exploration: Same question as in (6) above, but this time write the area of △ABC in terms of a, c, and B.
Exploration: Same question as in (6) above, but this time write the area of △ABC in terms of a, c, and B.
You have now derived the formula for the area of a triangle provided Side-Angle-Side. You will use this formula in Lesson 10-5.
