Deriving the Area of an Obtuse Triangle You just derived theformula for the area of an acute triangle using trigonometricratios. Now extend the idea to finding the area of an obtusetriangle.

Part A

Draw a line that passes through points A and B. Then draw a linethrough point C that is perpendicular to line AB . Label theintersection of the perpendicular line AB and as point D. Take ascreenshot of your construction, save it, and insert the image inthe space below

Part B

What do you know about ΔBCD?

Part C

In terms of the trigonometric ratios for ΔBCD, what isthe length of CD ? Insert text on the triangle in GeoGebra to showthe length of CD . Take a screenshot of the triangle with thetext,save it, and insert the image in the space below.

Part D

Using the formula 1/2 base x height, write an expression for thearea of ΔABC. Base your answer on the work you did inparts A through C. Show your work.

Part E

Compare the formula for the area of the obtuse triangle in partD with the formula for the area of an acute triangle in task 1,part J. How do the formulas compare?

Part F

You found one formula, area of triangle = 1/2 acsin(B) , thatapplies to an obtuse triangle just as it does to an acute triangle.Which other formulas for the area of an obtuse triangle can youderive? Show the formulas and justify your answer. (Hint: See task1, part K.)

Part G

Using your own words, describe the formula for the area of anobtuse triangle in word form.

Part H

Based on the formulas for an acute triangle in task 1 and theformulas for an obtuse triangle in task 2, can you draw a generalconclusion about the area formulas for any kind of triangle: acute,obtuse, or right?