SOLUTION: Thanks for your help in advance. Here is the photo of the triangle and sink hole: https://byuis.brainhoney.com/Resource/46824920,0/Assets/Media/Images/41.4-HOT4-Sinkhole.jpg A

Question 1040826: Thanks for your help in advance. Here is the photo of the triangle and sink hole: https://byuis.brainhoney.com/Resource/46824920,0/Assets/Media/Images/41.4-HOT4-Sinkhole.jpg

An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sink hole without falling in so you use congruent triangles. You have one piece of rope that is 50 ft. long and another that is 70 ft. long. You pick a point A on one side of the sink hole and B on the other side. You tie a rope to each spot and pull the rope out diagonally back away from the sink hole so that the two ropes meet at point C. Then you recreate the same triangle by using the distance from AC and BC and creating new segments CE and CD. The distance DE is 52.2 ft.
a. What type of triangles have you created?
b. How do you know the triangles are congruent?
c. What is the measure of $\footnotesize{\angle ACB}$?
d. How far across is the sink hole?
e. What is the perimeter of $\footnotesize{\triangle ABC}$?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The triangles are congruent by SAS.

The perimeter of one of the triangles is 172.2 feet. 180 divided by 172.2 gives roughly 1.045 degrees per unit measure of side length, so since the side opposite angle C measures 52.2, angle C is approximately 54.56 degrees.

John

My calculator said it, I believe it, that settles it

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