Geometry 10-5a GeoGebra Primer: Triangle Area & The Law of Sines

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: 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: 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: 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: 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: 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: Same question as in (6) above, but this time write the area of △ABC in terms of a, c, and B.