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Question 1111727: Hello tutors! I am extremely confused on this question it would be extremely appreciated if you guys can help me out... again I really appreciate your help and what you do here! This link leads to the question
https://docs.google.com/document/d/1MTDEdNJazocnHEmBvYzJDl-8yjM-Wpn74E0itR0N0JY/edit?usp=sharing
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the two triangles are congruent triangles.
they are congruent by SAS
SAS means corresponding sides and the angle between them are congruent.
AC = CE because you made CE the same length as AC.
BC = CD because you made CD the same length as BC
angle ACB is congruent to angle DCE because they are vertical angles and vertical angles are congruent to each other.
the measure of angle C is 48.0963477 degrees.
this was found through the use of the law of cosines.
law of cosines says c^2 = a^2 + b^2 - 2ab * cos(C)
formula becoms 52.2^2 = 50^2 + 70^2 - 2 * 50 * 70 * cos(C)
solve for cos(C) to get:
cos(C) = (52.2^2 - 50^2 - 70^2) / (-2 * 50 * 70)
solve for cos(C) to get:
cos(C) = .66788
solve for C to get:
angle C = arccos(.66788) = 48.0963477 degrees.
since the triangles are congruent, and since corresponding sides of congruent triangle are congruent, then the distance across the sink hole, which is AB, is the same distance of the line segment DE, which is 52.2 feet.
the perimeter of triangle ABC is the same as the perimeter of triangle DCE, which is equal to 70 + 50 + 52.2 = 172.2 feet.
you didn't need to, but you can also solve for the other two angles using the law of sines.
i did, and then added up all 3 angles and got the total equal to 180 degrees, as it should have been.
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