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marlenerojas201
21.06.2019 •
Mathematics
Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?
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Ответ:
Part A) The triangles ABC and EDC are similar by AAA, because the three internal angles are equal in both triangles
Part B) The width of the river is about![39\ ft](/tpl/images/0001/1972/483ba.png)
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent
Part A) we know that
In this problem , triangles ABC and CDE are similar by AAA, because its corresponding angles are congruent
so
m<DCE=m<ACB -----> by vertical angles
m<EDC=m<ABC -----> is a right angle
m<DEC=m<CAB -----> the sum of the internal angles must be equal to 180 degrees
Part B) we know that
The triangles ABC and EDC are similar -------> see Part A
therefore
substitute the values and solve for AB
Ответ:
the answer to the first one is b,c