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

Last updated about 4 years ago

7 Nsɛmmisa

Slide the Slide Me! slider in the applet below then begin the items that follow.

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The same applet from above is embedded again for your convenience.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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7.

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