Question 1117669: Consider and trapezoid in the following image and use them to answer the questions below. is a right triangle and trapezoid is isosceles. Do NOT use the law of cosines, use our knowledge from the content of this course.
https://api.agilixbuzz.com/Resz/~PW4LEAAAAAg0mvm0m9wE0B.X2QsVlPtegqSvwegHlyxOB/48780738,5CF,0,0/Assets/Media/Images/41.6-HOT1-Proofs.jpg
a. Describe how to find the lengths of segments x, y, and z . Show your answers for this question. Explain how you can be confident your calculations are correct.
b. Describe how to find the angle measures of angle DEG, angle DGE, angle EDG and angle ABC . Explain how you can be confident your calculations are correct.
c. Are there any segments or angles you can’t calculate based solely on the information in the image? Why?
d. If we drew a median into trapezoid DEFG and the given measurement of that median was 21.425, would that change your answer for part c of this question?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is an isosceles trapezoid, because the two angles are supplementary on the right side.
y is 25 based on the Pythagorean theorem
w is sqrt (850)=29.15
z must be 15
Making a right triangle to look at the altitude
cos 59=a/15, so a is 7.73 between the right corner and the edge of x
That means x is 29.15-2(7.73)=13.69
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The median should be half way between 13.69 and 29.15
That is half their sum, or half of 42.84 or 21.42
That doesn't change the answer above
Once I know the trapezoid is isosceles, the angles at the base have to be 59d and the angles at the top 121d.
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